Black Hole Perspectives

Black Hole Perspectives

by John Michael Williams

[email protected]

2011-02-19

A nonmathematical thought experiment provides insight into what it might be like inside and

outside of a black hole.

Copyright (c) 2011, John Michael Williams. All rights reserved.

J. M. Williams 2011-02-19 page 1

Preface

Everything in this essay is intended to be physically correct, although it represents the author's particular reasoning and is subject to criticism based on prevailing opinions, some of which, in turn, may be based on inconsistent applications of mathematics. Because no black hole can be observed except by its gravitational influence on other objects, some arguments and calculations in the literature must be accepted as much on mathematical faith as on evidence.

Readers wanting some simplified mathematics to support the theory behind the discussion in this essay should read the excellent presentation on relativity by Christoph Schiller, Motion Mountain: The Adventure of Physics,Volume II, which is downloadable at http://www.motionmountain.net/mmdownload.php?f=motionmountain-volume2.pdf.

Black holes remain a complex and sometimes controversial subject in astrophysics. This essay ignores quantum effects near the event horizon and just touches upon questions of whether time might be reversed, in some sense, inside a black hole. The idea of low-mass "little black holes", in which energy density alone could create a gravitational event horizon, is proposed solely to implement a thought-experiment neutrino detector.

Basic Assumptions

We assume here that the reader has some familiarity with the basics of relativity theory: The speed of light in vacuum is the maximum, limiting speed -- nothing can move at a speed faster than light. Also, the speed of light always is the same, constant value, c, no matter how or by what instrument that speed is measured.

Along these same lines, it must be understood that accelerating an object to a very high velocity in a particular reference frame, adding energy to that object, causes it to experience time dilation and length contraction relative to other objects not accelerated in that reference frame. Time dilation means that time for the accelerated object passes more slowly than for unaccelerated objects, as measured from an unaccelerated object. Length contraction means that the length of the accelerated object becomes less in the direction of motion when measured from an unaccelerated object.

These effects, time dilation and length contraction, are relativistic: In other words, they are relative to ones point of view. When measured within an accelerated object, time, which is to say proper time, passes at a normal rate and is not dilated; however, time is compressed, passes more rapidly, for unaccelerated objects when measured from the accelerated object. Likewise, unaccelerated lengths become greater, are expanded, when measured from the accelerated object.

It has been confirmed again and again, by experiment, theory, and observation, that there is no possible vacuum frame of reference, no fixed structure or coordinate grid in space, except as shared locally by objects not (a) moving or (b) accelerating in any


significant way relative to one another and not (c) in significantly different gravitational fields.

The Home Object

We begin our thought experiment by imagining a very dense, very massive object in space which we shall call the Home Object. This object, perhaps something like a neutron star, is spherical, fairly small, say 10 kilometers (km) in radius, and extremely massive. The Home Object does not rotate, and it is almost homogeneous, with maybe some minor lumpiness and layering of structure from place to place within it.

At the very center of the Home Object, there resides an observer. Because the mass of the Home Object is symmetrical about the observer, the pull of gravity at its center cancels out and is zero. However, the weight of the overlying matter creates an enormous pressure on the observer, a pressure which we shall ignore for now.

The matter of which the Home Object is composed, whatever its nature, would make it opaque to light: Photons within such a dense medium would be scattered or absorbed completely. So, the observer could not see anything by light. However, like all matter, the Home Object would be much more transparent to neutrinos, tiny massive particles which travel almost at the speed of light. Neutrinos do not interact with anything except very rarely by the weak force. A neutrino could traverse a light-year of solid lead, and the likelihood that it would interact with a lead atom would be very small -- but not zero. Whatever the Home Object might be, we assume that it does not interact much with neutrinos -- specifically, we shall assume that a neutrino could pass through the Home Object with only about a 10% probability of an interaction.

In addition to being very transparent to neutrinos, let us assume that all the matter in the Home Object also emits neutrinos, making it slightly luminous (in neutrinos). We do not specify the presumably nuclear source of these neutrinos.

Our observer has a very special neutrino telescope which allows her to see: In our thought experiment, its sensitive surface is made of a grid of thousands of tiny, low-mass black holes. The black holes are held fixed rigidly and, like all black holes, absorb everything, even neutrinos, which intercept them. Every neutrino has momentum, and this momentum is transferred to any black hole which absorbs it. The resulting vibration of the black holes on their grid thus reports every neutrino reaching the telescope. Our observer can see by what, for brevity, we shall call "neutrino light".

Neutrinos are produced by high-energy cosmic rays and also by the nuclear fusion reactions which power the Sun and stars. Stellar neutrinos typically have an energy in the range of 5 to 15 MeV (million electron volts). We shall not care exactly what this energy means, but it does correspond to a specific quantum wavelength or frequency of each neutrino: A neutrino of 5 MeV will have a longer wavelength, and a lower frequency, than one of 10 MeV. A neutrino of 10 MeV will travel at a speed a little closer to the speed of light than one of 5 MeV; the speed is what makes the energy, wavelength, and frequency, differ.


Gravity and Neutrino Light

So, what can our observer see? Well, the Home Object itself will appear to be like a slightly tinted, luminous glass ball; she will see perhaps some of the lumpiness and layering and will be able to tell where the outer surface is. She also will be able to observe the external stars and galaxies beyond the Home Object. Whereas astronomy by light observes the hot surfaces of the stars, astronomy by neutrino light observes the hot neutrinos created in their cores.

But, there is a factor which we have omitted: Gravity. The Home Object has an enormous gravitational field. To move anything from the observer's location toward the surface of the Home Object would reduce the gravitational energy it would have gained by falling to the center; equivalently, if an object located near the surface could fall freely to the center, its energy would be increased enormously by gravity. It is the latter which determines, by relativity theory, that our observer will see objects distant from the center to experience time compression and length expansion, just as though the observer were moving at a high speed or were being accelerated strongly. Features of the Home Object near its surface will be seen by our observer as increased in length; and, the frequency of their emitted neutrino light will be raised because of time compression, making them appear "bluer" in neutrino color (because blue light has a higher frequency than red light).

So, our observer will see the radius of the Home Object as being more than 10 km, perhaps 50 km; and, more distant features of the Home Object will appear expanded away from one another -- increasingly expanded, the closer they are to the surface. As already mentioned, the neutrino light from the outer layers of the Home Object will be blue-shifted; the farther away, the bluer the shift.

Because a blue shift in general can be interpreted as being caused by a positive Doppler shift, a velocity directed toward the observer, our observer in principle could interpret the neutrino-light blue shift as an ongoing contraction of the Home Object. Thus, our observer could interpret her observations as meaning that the Home Object was collapsing, with the rate of collapse being greater, the greater the distance away. Alternatively, our observer could interpret the blue shift as an expansion of the central regions of the Home Object, bringing herself and her telescope toward the outer regions of the Home Object at an increasingly high speed.

Neutrino light from the stars also would be blue-shifted as it was accelerated and fell toward the surface of the Home Object, a process which would increase the speed of the neutrinos relative to the Home Object. After passing through the surface of the Home Object and reaching the telescope at its zero-gravity center, the acceleration from the Home Object would fall to zero, but a maximal shift to the blue would remain.


Pressure and GravityWe have decided to ignore the pressure of the Home Object upon our observer, but

what about the pressure elsewhere?

Pressure depends on weight, and, as we go farther and farther away from the center of the Home Object, the pressure decreases. Near the surface of the Home Object, the pressure is near its minimum; it still is substantial, because the force of gravity there is near its maximum, even if applied only to a few overlying layers of neutrons, iron atoms, or whatever other matter we choose to imagine for the Home Object.

Outside the Home Object

How would the Home Object look to a different observer, an astronaut, say, on a space ship more or less motionless and some thousands of km away? Well, assuming the surface of the Home Object to be cool, he could not see it except by reflected light. The astronaut could shine a light onto the Home Object; the surface might appear grey in color. A flux of neutrinos from the Home Object also might be detected.

Given the enormous gravitational field, the surface would appear more or less smooth and otherwise unremarkable. Photons from the space ship emitted toward the Home Object would gain energy from its gravitational field and thus be shifted toward the blue; when they were reflected, they would lose the same energy and be red-shifted back to their original color. Neutrinos emitted by the Home Object would be slowed down and delayed by its gravity, causing a shift to the red.

Near the surface of the Home Object, time would be compressed in the view of our internal observer, so actions taken by the astronaut would be seen by the observer to occur more quickly than expected. Conversely, actions taken by the observer would appear greatly slowed-down as seen by the astronaut.

Fig. 1. Time sketched at different locations in and around a massive object not a black hole. Left, compression in the frame of the internal observer. Right, dilation in the frame of the astronaut. Time unaffected by gravity

is at the extreme left in each figure.


Black Hole Basics

A black hole is a massive object with a gravitational field so intense that it attracts photons or anything else at the speed of light. Equivalently, any light leaving a black hole would be red-shifted to a frequency of zero. Light can not escape from a black hole, which is why it is called black. Depending on their distance and direction of propagation, photons originating from outside could be lost into the black hole, could orbit it, or simply could have their path of propagation bent by it.

For our purposes, we shall use the word mass to refer either to the rest mass m of massive particles or other objects, or, equivalently to the rest energy E as related by E = mc2 -- or, to any mixture of E and m. Both E and m have the same gravitational effects, as given by the equation.

To begin, it seems obvious that, because any black hole has a mass greater than zero, and contains many elementary particles (or a mass equivalent to many of them), its mass must occupy more than a zero volume of space. Even a Bose condensate of many particles could not reside at a single point. No matter how space might be distorted by gravity, there will be a nonzero volume occupied by the mass of a black hole.

Because light can not escape from the inside of a black hole, neither can anything else, including neutrinos. However, gravitational intensity decreases approximately as the inverse square of the distance from the center of mass of any object; so, at some distance from any black hole, the gravitational field necessarily will become low enough to allow light to escape. This boundary, at which light could escape, is called the event horizon of the black hole. It is like the horizon for a ship at sea: No one on the ship can see past the horizon, which is caused by the curvature of the earth. Likewise, no one outside can see past the event horizon of a black hole, which equivalently may be explained as a distortion of space caused by its gravitational field. The event horizon follows the black hole around, just as the horizon at sea follows the ship. Unlike, say, the Great Wall of China, a horizon is just a value of field strength; regardless of the associated distortion of space, it does not represent a physical feature or object. However, it imposes constraints upon the physics of the space around it.

So, an astronaut could shine light on a black hole, the light would go into the black hole, would meet the event horizon -- and nothing would come out. Our astronaut thus can not see a black hole, except by the fact that nothing else is visible at its location, and by other effects of its gravitational field on nearby objects or on light passing nearby.

Entry ForbiddenSuppose our astronaut observed a second astronaut falling into a black hole: Our

astronaut would notice an increasing time dilation as the infalling one approached the event horizon. If the infalling astronaut ever reached the event horizon, time would have been dilated to zero; this means that a clock carried by the infalling astronaut would have stopped ticking, as measured by, say, radio signals sent from the clock to our


astronaut. This, of course, can not happen during any finite time of observation by our astronaut.

Some authors assert that in the proper time of the infalling astronaut, he simply will pass through the event horizon – which, after all, is just a certain value of the strength of the gravitational field. Because photons emitted by the infalling astronaut are weakened to zero frequency, therefore the astronaut must be able to pass through the event horizon. This assertion not only is irrational but creates a topological inconsistency between the observations of the two astronauts.

The topological inconsistency arises because our astronaut never will see the infalling astronaut cross the event horizon, because time in the frame of our astronaut will be stopped at the horizon, preventing further spatial displacement.

If the infalling astronaut could cross the event horizon, we would have two inconsistent final states:

State 1: The second astronaut is inside the event horizon (in his own frame);

State 2: The second astronaut is not inside the event horizon (in the others frame).

Even allowing time to approach infinity as a limit for both astronauts would not resolve this inconsistency. There is a conceptual error here which also leads to errors in any application of mathematics to this problem. It is not a matter of observability but of a space-time interval in two different frames.

There are two obvious and simple reconceptions:

A. Apply only the proper time argument and extend it to the external astronaut's frame. This would require that the externally observed red shift on approaching the event horizon, which is a blue shift in the frame of the center of the black hole, somehow be continued to the interior. The infalling astronaut would vanish at the event horizon, in the view of our astronaut. The zero time at the event horizon would develop into an increasingly blue shift as the infalling astronaut, now inside the event horizon, continued to accelerate toward the center of the black hole. Otherwise, the infalling astronaut could not continue gaining gravitational energy. Locally, in the frame of an object at rest near the event horizon, either (a) speed would exceed c or (b) time would run backwards for the rest of the fall, or both, causing gross violations of the laws of physics, particularly thermodynamics, inside the event horizon.

B. Apply only the external observer argument and extend it to the proper time of the infalling astronaut. This would require that, in the frame of the infalling astronaut, (proper) time should pass normally during his free-fall acceleration, and he should notice that he continually was being speeding up, in reference to other objects outside the black hole. However, objects in the direction of the horizon would be increasingly blue-shifted; as he approached the event horizon, the remaining distance to it increasingly would be stretched in his frame, and no amount of proper time would allow him to reach it.


In the present work, the resolution is to assume that an infalling object can not reach the event horizon of a black hole in any frame of reference. This is a special case deducible from the more general assertion that a zero rate of passage of time is zero in any frame of reference. This may not be entirely satisfactory, but at least it does not require irrational, inconsistent, or unphysical assumptions.

Black Hole Anatomy

Tensor calculus could be used to project the shape of the gravitationally-distorted space of a black hole onto a three-dimensional Cartesian grid. However, we shall bypass the mathematics and just sketch how that space would appear. The procedure we shall use is consistent with typical physical analysis but may not be found in the astrophysics literature.

Fig. 2. Two-dimensional sketch of the gravitational field intensity in and around a black hole. No scale implied. The circular contours delimit a

region in which the gravitational field prevents light from escaping.

To explain this figure, we shall project circles representing Gaussian spheres. A Gaussian sphere in our figure is a three-dimensional boundary drawn around something in order to partition the problem space. A Gaussian sphere permits operations such as surface, line, or volume integration to be carried out conveniently. Such a sphere is a mathematical construction and has no physical property, including no lower limit on its size. We can use this approach to develop what we believe to be a correct conceptualization of the properties of a black hole.

Black Hole Gravitational Intensity

Gra

vity

y

x


We shall examine the meaning of the figure by centering a Gaussian sphere on the center of gravity of a black hole, which is projected in Figure 2 to the center of the concentric contour circles, at x = y = 0. In three dimensions, this would be x = y = z = 0, the same as r=0 in spherical (polar) coordinates. The actual shape of our Gaussian sphere in the gravity-distorted space of the black hole will be symmetrical but otherwise is irrelevant.

If we let the radius of our Gaussian sphere shrink toward zero, eventually we shall have a sphere so small that it will enclose part of, but not all, the mass in the black hole. This could be indicated in Figure 2 by a circle not shown but inside the smaller contour circle.

After enough additional shrinking, our sphere almost will be a point and will enclose a negligible amount of the black hole mass. Because the mass outside of the sphere is symmetrical, its gravitational field will cancel out to zero, leaving only the field caused by the mass inside of the sphere. Thus, the gravity on the surface of this Gaussian sphere will be negligibly different from zero. This is indicated by the central minimum of the surface plot in Figure 2. Light could cross this sphere in any direction.

If we now begin to increase the radius of our Gaussian sphere, it will enclose more and more mass, making the gravitational field on its surface increase. This is indicated by the region of the surface plot between the central minimum and the level projecting to the smaller circular contour. At some point, our sphere will enclose enough mass to make the field so strong that it will not permit light to exit across the surface of the sphere. This makes the radius of our sphere equal to the radius of what we shall call, the internal horizon. This horizon is indicated by the inner circular contour.

If we continue to increase the radius of our sphere, the field strength will continue to increase; but, eventually, we shall run out of mass, and the field on the surface of our sphere will begin to decrease. This is indicated by the region outside and just below the annular maximum of the surface plot. Light can not propagate from the inside to the outside of this sphere. After further increase of the radius, the field will drop down to an intensity at which light can exit the Gaussian sphere. Just inside this sphere, then, will be the event horizon of the black hole. This horizon is indicated by the outer circular contour.

A Gaussian sphere larger than the event horizon will reside in normal space, familiar to our common experience but possibly somewhat distorted by gravity. Light can travel in any direction across this last sphere.

HorizonsA horizon is a local limit on propagation; it does not depend on differences in the

gravitational field but on the intensity of the field. The speed of light, c, also is a local limit, but on speed of propagation.

In a strong gravitational field, such as that just outside an event horizon, observers who are not much separated in space will not see much frequency shift or time or length change in regard to each other. To experience time dilation or length contraction, one


observer must be in a gravitational field which is substantially stronger than that of the other; this requires significant separation in space, the field being assumed to vary only spatially. The greater the (radial) spatial separation, the greater the time dilation and length contraction.

However, an observer near a horizon will be limited by the horizon no matter what the distance to it. A photon emitted by an external observer toward the horizon will be blue-shifted and would vanish if it could reach the horizon, no matter how close the observer might be. The observer would see the photon as red-shifted, if it was scattered before it reached the horizon, as previously discussed. Likewise, a photon emitted by an internal observer toward the horizon will be red-shifted to zero and vanish if it could reach the horizon, no matter how close the observer might be.

The meaning of "vanish" in this last case is that photons are not massive and have no inertial frame; so, a photon emitted from inside a black hole toward the horizon would be red-shifted to zero if it could reach the horizon and presumably would be annihilated. The total momentum and energy of the original photon then will have been transferred gravitationally to the black hole. By contrast, a neutrino emitted the same way will be red-shifted and decelerated to zero speed and a very low quantum frequency but will continue to exist. The neutrino could not possibly reach the horizon. The neutrino then will reverse its direction and be accelerated toward the center of the black hole, gaining speed and increasing in quantum frequency until it eventually is scattered or absorbed.

The question of a photon emitted within the event horizon is a complex one. One might argue that, as a photon approached the horizon from the inside direction, along a radius of the black hole, the photon would be red-shifted relative to the frame of the center of the black hole, the horizon would be more and more blue-shifted, distance to the horizon would be stretched, and the photon merely would continue with a speed of c forever, never quite reaching the horizon, but retaining its velocity (and quantum numbers). However, this argument is flawed, because a photon has no inertial frame relative to which it can be shifted; in all previous discussions, photons are described as red- or blue-shifted relative to some inertial frame. A photon has no proper time and never can reverse its direction or otherwise change the velocity with which it was created: It can only follow its original path in space, however distorted by gravity that space might be. So, a photon could be redirected toward the center of the black hole because of the distortion of space, but not because its speed was just c. There is no way that a red shift relative to the center of the black hole could be changed into a blue shift "relative" to the photon. Photons mediate space-time measurements in relativity theory; they do not obey its transformation laws.

Likewise, a photon approaching a horizon from outside would have been blue-shifted in the frame in which it was created as evidenced locally by scattering or any other interaction; but, the scattering would be observed from the location of its creation as red-shifted by time dilation and length contraction.

A related but equally invalid argument is that gravity stretches space so much at the horizon, that an upward-directed, internally emitted photon would end up "running in place", with space (the vacuum) differentially flowing past it at the speed c, continually


being "absorbed" by the black hole. Thus, a photon could reach the horizon and not be annihilated, but it would be stuck there. This cannot be correct, because the vacuum never can have a velocity or direction; if it could, this would imply an absolute reference grid for the vacuum, and relativity would not work.

In this essay, we prefer the simple argument that internally emitted photons directed away from the center of the black hole would be increasingly red-shifted in every internal frame, time would be dilated increasingly in every internal frame, and for this reason, only, the photon never quite would reach the internal horizon. This argument does not depend on calculations of general relativity per se.

In any case, approach from inside or outside, we would have a photon changing in frequency and energy, depending on the location of the scattering interaction of the photon with something else. Such an interaction would, of course, destroy the photon. However, it seems unavoidable that, at a horizon, time would be stopped and photons reaching the horizon, if they could, would be annihilated because the horizon was there.

Horizon MovementOther things being equal, if the mass of a black hole is increased, the event horizon

will grow in radius. If a substantially massive object approaches the event horizon, the horizon will retreat, as seen externally, because some of the gravitational field of the black hole will be cancelled by the oppositely directed field of the other object. At a large distance, the gravitational field will obey the inverse-square law and will take on a zero value at some point between the event horizon and the nearby object. As the object approaches the black hole, the zero field point will shift to the inside of the approaching object; eventually, there no longer will be any zero field nearby.

Fig. 3. Vector-sum calculation of the effect of a large nearby mass on the gravitational field of a black hole. Square-law approximation. The zero field between the black hole and the two massive bodies is

on the line between the two centers of gravity and inside the small near-zero ellipse between them. For simplicity, the surface plots omit the central minimum of Figure 2.


While the very massive object is nearby, other smaller masses which originally were between it and the black hole and had come very close to the original event horizon will continue to be attracted to the black hole and will follow the retreating horizon inward, as seen externally.

If the very massive object passes away, the event horizon will return to its original shape. After this, although time in the external frame almost has stopped for the smaller masses, it has not for the event horizon; the latter then may expand past those masses, putting them inside the horizon.

This is one mechanism by which a black hole might grow, avoiding the topological inconsistency described above. Gravitational fields of all external, astronomical objects continually will cause any event horizon to vary this way, at least microscopically, allowing time-dilated mass just outside of the event horizon to cross it without requiring external time to pass through zero. Once inside the event horizon, nothing can exit the black hole in any direction. The precise ballistic behavior of masses just within the event horizon is left undefined in the present work, but they might be time-frozen in place or displaced gravitationally in (external) space toward the center of the black hole.

Speculatively, a massive object which just barely was a black hole might have internal and event horizons almost superposed. A massive object passing nearby, then, hypothetically might be able to push the event horizon below the internal horizon, exposing matter within the black hole to external influences, allowing photons or massive particles to exit the black hole, and perhaps causing such a black hole to become an object in normal space.

The central singularity of a black hole will be discussed more below; but, for now, imagine that the mass of a black hole could occupy enough volume to permit the spatial arrangement of that mass to change its shape in some meaningful way. Then, even more speculatively, nearby passage of a massive object possibly might cause oscillations of the event horizon if the mass of the black hole rearranged itself elastically to accommodate the local change in the event horizon.

The Home Object Black Hole

Accepting all the previous assumptions and discussion, what would happen if we changed the Home Object into a black hole?

Our Home Object might be changed into a black hole (a) by making it contract to increase its density, or (b) by adding mass, for example by collision with a star or other massive object. Or both. Coincidentally, notice the similarity here between making a black hole and detonating a nuclear-fission bomb.

Anyway, let us assume that our Home Object instantaneously but gently has been added some mass in its interior but not too far from its surface. We shall assume that as a result, the Home Object now is a black hole with an event horizon radius just over 10 km as seen externally, so that its newly formed event horizon is some small distance above what previously was its surface.


Black Hole View from OutsideNeutrinos, or anything else emitted by the astronaut and massive, would be

accelerated toward the Home Object and also would be increasingly red-shifted in the frame of the astronaut as they neared the event horizon. Photons emitted toward the Home Object would be red-shifted in the frame of the astronaut but not changed in speed (because c is a constant); however, gravitational distortions of space could make the paths of photons apparently curved, as inferred by the astronaut.

At the event horizon, in the frame of the astronaut, time would be dilated to zero by the Home Object's gravitational field, and no further change could occur. The thickness of the event horizon would be shrunk to zero because of length contraction. The event horizon, or, more accurately, the region just outside of it, might glow because of interactions among the highly accelerated particles and macroscopic objects attracted to it and colliding with each other just above it. These interactions could produce photons, neutrinos, electrons, or other particles; and, the closer they were to the event horizon, the slower their rates and the redder their wavelengths would be, as viewed by the astronaut.

As energy from external sources continued to impinge upon the event horizon, the gravitational field would strengthen, and the diameter of the event horizon would increase. As mentioned above, the event horizon is just a particular value of the field intensity; it can shift in and out, depending on changes in the black hole's gravitational field. Thus, physical entities, particles or fields other than the gravitational field, can be moved between the inside and the outside of the event horizon because of changes in the horizon radius. We shall treat this effect as negligible, for our purposes. In all other respects, once the black hole had been formed, it would appear about the same to the astronaut for an indefinitely long period of observation.

The time dimension is measured as a scalar, and all scalar zeroes are the same; so, time would be dilated to zero at the event horizon not only for the astronaut but for anyone in any reference frame.

Keeping all this in mind, let's see how our internal observer has been doing.

Black Hole View from InsideAt the moment the Home Object became a black hole, assuming the additional mass to

have been added near the outer regions of the Home Object, our observer still would see the neutrino-luminous internal lumps and layers of the Home Object as before, but they would be increasingly blue-shifted in neutrino color until they almost reached the internal horizon, the radial distance from the center of the Home Object at which the gravitational field shifted light to zero frequency. For the new black hole, this distance now would be astronomical, because of length stretching in the regions farthest from the observer. At the distance of the internal horizon, time would be dilated to zero, as at the event horizon, and nothing more could change there in any reference frame.

Notice that our thought experiment for this moment implies two horizons, an external event horizon and an internal horizon, both outside the observational realm of the


internal observer. This is because of the way we are assuming that the black hole was created. There is some controversy over how any black hole might be created, but we shall ignore this in the present essay, although it raises questions concerning the consistency of the mathematics applied.

In general, in an external frame of reference the same as that of the astronaut, the two horizons would be at different radial distances from the center of our black hole at the moment of its formation. See Figure 2 above. The event horizon would be located at the (approximate) square-law distance from the center of the black hole at which light almost can escape. The internal horizon would be located at the radial distance inside the black hole at which light first ceases to be able to escape. The internal horizon obviously can not be located at the center of the Home Object, because the total mass between there and the center would be zero by definition. However, mass or density must have been increased in the regions inside the internal horizon, or a black hole could not have been formed.

Because neutrinos are not massless, like photons, time compression affects their speed as well as their quantum frequency. So, as she looked closer and closer toward the internal horizon of the Home Object, not only would our observer see the Home Object's neutrinos shifted increasingly to the blue, but they increasingly would be originating from more and more distant sources and speeded up. The neutrino flux per unit visual angle from distant regions, near the internal horizon, would be reduced greatly, because length stretching would reduce the apparent density of the matter of which the Home Object was composed. Neutrinos can't move quite at the speed of light, so, momentarily, just inside the internal horizon, no emitted neutrino could escape upward, and they all would be drawn downward. The distance to the internal horizon itself effectively would be infinite, and everything there would be featureless neutrino blackness.

If this state could endure long enough, a neutrino beam directed upward by the internal observer would be red-shifted down to zero speed just inside of the internal horizon; the neutrino particles would fall back toward the center, the same way that a ball tossed into the air falls back to the ground. If upward-directed neutrinos were reflected by some feature inside the internal horizon, the reflected neutrinos would be red-shifted on the way up and then blue-shifted by the same amount as they returned; thus, they would be detected at the same energy (= same wavelength and frequency) as that at which they had been emitted.

No light or neutrinos from beyond the internal horizon could be seen at the center, because time at that horizon would be elapsing at zero rate both in the frame of the observer and of the astronaut -- and of anyone else.

However, in the observer's view, time just inside of the internal horizon would be compressed to an enormous rate, speeding up the rate of neutrino production and making that region of the Home Object briefly very neutrino-bright. Very soon though, whatever reaction(s) had been producing the Home Object's neutrinos would have died out because of limited half-life(s), and neutrino blackness would begin to spread inward from the internal horizon, at a rate declining with the decline in time compression as the distance to the center became smaller.


The respective rates of passage of time for the internal observer and the astronaut shortly after formation of the black hole are sketched (not to scale) in the next figure:

Fig. 4. Time, sketched after formation of the Home Object black hole. Left figure, for the internal observer; right figure, for the astronaut. Areas respectively not visible are shaded. Time unaffected by gravity is at the

horizontal dotted line, but the relationship between the clock rates is arbitrary, because of the discontinuities which make communication or normalization impossible across the horizon(s).

Telescopic Catastrophe

Upon creation of the black hole, the astronaut would see a red shift to zero at the event horizon. In his reference frame, just after the Home Object had become a black hole, the matter in the Home Object located between the two horizons would be frozen permanently and never would change again. Light could not propagate; all the exchange bosons which mediate the fundamental forces of physics would be stopped. This idea of a timeless zone between the horizons extends the boundaries of the zone to its interior and is quite arbitrary: At a minimum, because each of the horizons creates a zero-time boundary, nothing happening between them could have any effect anywhere else, except gravitationally to move the horizons themselves.

But, there would be the mass of a black hole inside the internal horizon. Everything so far described has been referred to a brief period, in the frame of the astronaut, after the Home Object had become a black hole. However, immediately thereafter, one must consider the effect of the mass inside the internal horizon. In the view of our internal observer, there would be a tremendous flux of radiant energy, followed by an infalling of all the matter inside the internal horizon, possibly initially as a shapeless waterfall of blue-shifted quarks and leptons. The distance from the center almost to the internal horizon, although vastly expanded, eventually would allow a violent pressure wave to propagate throughout the Home Object, destroying its preexisting structures, but bounded by the internal horizon. Although no further change would be visible to the astronaut; in the frame of our observer, she would be killed and her telescope ruined.

The actual process would be somewhat as follows: Just inside the internal horizon, the force of gravity would be so great that nothing massive could support itself. The material of the Home Object just inside the internal horizon would be compressed by gravity, causing the internal horizon to contract. The annular timeless region between


the event horizon and the internal horizon would grow downward. Probably, some massless or very light particles -- photons, gluons, maybe neutrinos -- previously inside the internal horizon would be left behind in the growing timeless region. But the contraction would continue almost without limit, the contents of the internal horizon being compressed physically like a reversal of the cosmological Big Bang, and total mass of these contents decreasing somewhat because of particles stranded in the timeless region.

The Result

The internal horizon would reach a collapsed state. As the radius of the internal horizon, in the frame of the astronaut, shrank gravitationally to a far smaller size, its contents would become a soup of energy; and, whether this soup included massive particles would be irrelevant.

No SingularityMathematically, many authors have used general relativity to infer that the center of

the black hole quickly would become a "singularity" -- in other words, a gravitational intensity effectively equal to infinity and perhaps limited in spatial volume only by quantum uncertainty. Applying this argument to the present approach, these authors would assert that Pauli exclusion would fail and only the Heisenberg uncertainty principle could prevent further increase in the extent of the timeless region. The internal horizon of the black hole would reach a microscopic but more or less stable size but would not quite collapse to a point.

However, this assumption seems physically very unlikely, because it presumes no increase in entropy during the collapse. In other contexts, increasingly extreme conditions begin to evoke new, usually nonlinear, physical processes which cause the primary driving cause, in this case energy density under gravitational force, to become less and less effective. Probably, as the inner horizon shrank, other effects not seen in normal space would prevent the physics from collecting all the energy at a mathematical point, even one limited to a finite extent by quantum uncertainty.

One possible nonlinearity might be caused by gravitons. These are hypothetical exchange particles which mediate gravity. They cause, or perhaps are equivalent to, the distortion of space in strong gravitational fields. If they exist, in extreme energy density or in extremely intense gravity, gravitons might begin to scatter off one another, decreasing the gravitational coupling to the rest of the energy and thus limiting the collapse. Or, maybe some threshold density of gravitons would begin pulling virtual photons or neutrinos out of the vacuum, again causing the collapse to stop before it was limited by quantum uncertainty.

Gravitons themselves entail conceptual difficulties. For example, if they are massless, they should be limited to propagation at the speed of light. But, then, how would a black hole exert a gravitational force beyond its event horizon, if gravitons were prevented by its gravity from leaving it? Or, does the speed of light not limit the speed of a graviton?


Do gravitons somehow not couple to gravity either as energy E or mass m -- does E = mc2 not apply to them? After all (see next paragraph), the speed of light, c, is used to define only the electromagnetic properties of the vacuum; gravity is not electromagnetic, so perhaps there are other vacuum properties which govern the speed of gravity?

Do gravitons propagate in a flat space, subject to special relativity but undistorted and unaffected by gravity?

Another possible nonlinearity might be caused by changes in the properties of the vacuum itself. For example, by definition, the speed of light c=1 /0⋅0 , in which the right side represents vacuum electromagnetic properties. Under increasingly extreme conditions, these properties might change, and the speed of light suddenly might increase, as it is guessed to have done during the similarly extreme inflationary period of the early phases of the Big Bang model of the formation of the universe. Such an increase might restore Coulomb repulsion or Pauli exclusion disproportionately and halt further gravitational contraction.

Something physical surely will arise which would dull the point of the mathematical singularity.

The Rest of the CatastropheAnyway, regardless of the final volume occupied by the central minimum inside the

inner horizon, in the frame of the astronaut, after the black hole had settled down, one could ignore quantum effects and imagine a new, now very small, internal observer. This observer again could be located at the center of gravity of the Home Object, with a newly rebuilt telescope. But, it couldn't be a neutrino telescope, because the region of the black hole inside the internal horizon would have been compressed and contracted into a tremendously concentrated energy bath; neutrinos probably could not propagate if they could exist, and the entire black hole, everything inside of the event horizon, would be impenetrable to photons.

The astronaut could not see inward past the event horizon, and there would be nothing for the new observer to see at all. For the new observer, the internal horizon would be a black nothingness located effectively at infinity, surrounded by indescribably intense energy. The gravitational field of the Home Object, changed into a black hole, has divided the universe into two partitions, separated by timeless walls, which no longer can communicate with one another.

Inside the Home Object, our new observer might conclude that she, her telescope, and the inner layers of the Home Object were being expanded outward, causing features at more distant regions to be increasingly blue-shifted. The concomitant length-stretching would make the Home Object radius appear limitless. She might conclude that her Home Object was undergoing an unknowable transformation which she might call, the Big Bang.

Black Hole Perspectives

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