19 April 2005 AST 2010: Chapter 23 1 Black Holes & Curved Spacetime.

11AST 2010: Chapter 23AST 2010: Chapter 2319 April 200519 April 2005

Black Holes Black Holes &&

Curved Curved SpacetimeSpacetime

19 April 200519 April 2005 AST 2010: Chapter 23AST 2010: Chapter 23 22

Questions about Black Questions about Black HolesHoles

What are black holes?What are black holes?

Do they really exist?Do they really exist?

How do they form?How do they form?

Will the Earth someday be sucked into a black Will the Earth someday be sucked into a black hole?hole?


Introduction to Black HolesIntroduction to Black HolesAt the end of a At the end of a massivemassive star’s life, its outer layers are star’s life, its outer layers are blown off in a (Type II) blown off in a (Type II) supernovasupernova explosion explosion

If the If the core remnantcore remnant has a mass greater than 3 has a mass greater than 3 MMSunSun, ,

then not even the super-compressed degenerate then not even the super-compressed degenerate neutrons can support the core against its own weight neutrons can support the core against its own weight

Consequently, according to theories, gravity Consequently, according to theories, gravity overwhelms all other forces and crushes the core overwhelms all other forces and crushes the core until it is infinitely small until it is infinitely small

The resulting point-like object is a The resulting point-like object is a black holeblack hole

Only the most massive, very rare stars (with Only the most massive, very rare stars (with initialinitial masses greater than 40 masses greater than 40 MMSunSun) will form black holes ) will form black holes

when they diewhen they die


General RelativityGeneral RelativityUnder the extreme circumstances of a black hole, Under the extreme circumstances of a black hole, Newton’s theory of gravity is inadequateNewton’s theory of gravity is inadequate

Newton’s theory works well in ordinary situations Newton’s theory works well in ordinary situations (motions in everyday life, planetary orbits, etc), but it (motions in everyday life, planetary orbits, etc), but it fails whenfails when

gravity becomes extremely stronggravity becomes extremely strong

large masses move very rapidlylarge masses move very rapidly

light is affected by a huge masslight is affected by a huge mass

To understand what black holes are, we begin with To understand what black holes are, we begin with an introduction to Einstein’s theory of an introduction to Einstein’s theory of general general relativityrelativity

It improves on Newton’s theory of gravityIt improves on Newton’s theory of gravity


The Equivalence Principle (1)The Equivalence Principle (1)The The equivalence principleequivalence principle says that life in a says that life in a freely fallingfreely falling laboratory is laboratory is indistinguishableindistinguishable from, and hence equivalent to, from, and hence equivalent to, life with no gravitylife with no gravityNo experiment can be done inside a sealed laboratory to No experiment can be done inside a sealed laboratory to determine whether it is determine whether it is floating in space without gravityfloating in space without gravity or or falling freely in a gravitational fieldfalling freely in a gravitational field

In other words, the two situations are In other words, the two situations are equivalentequivalent

In the absence of air friction, the boy and In the absence of air friction, the boy and girl on the right fall downward at the same girl on the right fall downward at the same rate (their speeds increase by the same rate (their speeds increase by the same amount each second), and so does the amount each second), and so does the ball if they aim it straight at each other ball if they aim it straight at each other

Consequence Consequence of theof the equivalence principle equivalence principle: : if the three are isolated in a box that is if the three are isolated in a box that is falling with them, no one inside it will falling with them, no one inside it will will be aware of any gravitywill be aware of any gravity


The Equivalence Principle (2)The Equivalence Principle (2)When a space shuttle is in When a space shuttle is in free-fall orbit around the free-fall orbit around the Earth, everything inside the Earth, everything inside the shuttle either stays put or shuttle either stays put or moves along a straight line moves along a straight line because gravity appears to because gravity appears to be absent inside the shuttle be absent inside the shuttleTo the astronauts inside it, To the astronauts inside it, falling freely around the falling freely around the Earth creates the same Earth creates the same effects as being far off in effects as being far off in space, remote from all gravitational influencesspace, remote from all gravitational influences

In other words, the astronauts feel weightless in such orbitIn other words, the astronauts feel weightless in such orbit

Thus the effects of gravity can be compensated by the Thus the effects of gravity can be compensated by the right accelerationright acceleration


Here’s the RubHere’s the RubIf a laser beam is sent from the back of a shuttle to the front, If a laser beam is sent from the back of a shuttle to the front,

in zero gravity the laser will hit the front center of the shuttlein zero gravity the laser will hit the front center of the shuttle

in free fall around the Earth the laser must also hit the front in free fall around the Earth the laser must also hit the front center, according to the center, according to the equivalence principleequivalence principle

but from the time the light left the rear wall until it reaches the front but from the time the light left the rear wall until it reaches the front the shuttle has moved!the shuttle has moved!

Thus the Thus the equivalence principleequivalence principle would seem to imply that light would seem to imply that light is bent by gravity!is bent by gravity!

Since light has Since light has nono mass, this would contradict the expectation mass, this would contradict the expectation that only objects with mass are influenced by gravity that only objects with mass are influenced by gravity


Einstein’s Radical IdeaEinstein’s Radical IdeaHe suggested that the light curves down to meet the front He suggested that the light curves down to meet the front of the shuttle because the Earth’s of the shuttle because the Earth’s gravity bends the gravity bends the fabric fabric of space and timeof space and time Any Any eventevent in the universe can be pinpointed using the in the universe can be pinpointed using the three dimensions of three dimensions of spacespace (where?) and the one (where?) and the one dimension of dimension of time time (when?)(when?)Einstein showed that Einstein showed that

there is an intimate connection between space and timethere is an intimate connection between space and timewe can build a correct picture of the physical world by we can build a correct picture of the physical world by considering the two together, in what is called considering the two together, in what is called spacetimespacetime

According to his theory, called According to his theory, called general relativitygeneral relativity, , the presence of mass (gravity) curves or warps the fabric of the presence of mass (gravity) curves or warps the fabric of spacetime spacetime the stronger the gravity (the larger the mass) is, the more the stronger the gravity (the larger the mass) is, the more spacetime is curved or warpedspacetime is curved or warped


Gravity Bends Spacetime Gravity Bends Spacetime (1)(1)

When an object (an electron, a space shuttle, or a light When an object (an electron, a space shuttle, or a light beam) enters a region of spacetime distorted by the beam) enters a region of spacetime distorted by the presence of another object’s mass, the path of the first presence of another object’s mass, the path of the first object will be different from what it would have been in object will be different from what it would have been in the absence of the second’s mass the absence of the second’s mass

In summary, In summary, matter tells spacetime how to curvematter tells spacetime how to curve, and , and the the curvature of spacetime tells other matter how to movecurvature of spacetime tells other matter how to move

Three-dimensional analogy of spacetime:Three-dimensional analogy of spacetime:


Gravity Bends Spacetime Gravity Bends Spacetime (2)(2)


Gravity Bends Light’s PathGravity Bends Light’s Path


Tests of Einstein’s Theory of General Tests of Einstein’s Theory of General Relativity (1)Relativity (1)

Since Newton’s theory is inadequate when gravity is very Since Newton’s theory is inadequate when gravity is very strong, Einstein’s theory can be tested where Newton’s strong, Einstein’s theory can be tested where Newton’s failsfailsThe motion of Mercury about the Sun provides a The motion of Mercury about the Sun provides a “laboratory” to test Einstein’s theory“laboratory” to test Einstein’s theory

Mercury’s orbit undergoes very slow, but detectable, Mercury’s orbit undergoes very slow, but detectable, rotation in spacerotation in spaceThis rotation cannot This rotation cannot be fully explained by be fully explained by Newton’s theory Newton’s theory Einstein’s prediction Einstein’s prediction was remarkably was remarkably close to the data, close to the data, giving him much giving him much confidence in his confidence in his theory theory



Einstein’s theory also predicts that Einstein’s theory also predicts that starlight is deflected starlight is deflected when it passes near the Sunwhen it passes near the Sun

If a star’s position is known when the Sun is not in the way, If a star’s position is known when the Sun is not in the way, then an observation of a shift in the star’s position when the then an observation of a shift in the star’s position when the Sun is in the way will confirm the theorySun is in the way will confirm the theory

Such an observation could be done during a total solar eclipse so Such an observation could be done during a total solar eclipse so that much of the Sun’s bright light is blocked outthat much of the Sun’s bright light is blocked out

The confirmation was made first in 1919 by British The confirmation was made first in 1919 by British astronomers and later by others! astronomers and later by others!



Einstein’s theory further predicts that the stronger the gravity, Einstein’s theory further predicts that the stronger the gravity, the slower the pace of time the slower the pace of time

In 1959, a comparison of time measurements on the ground In 1959, a comparison of time measurements on the ground and top floors of the physics building at Harvard University and top floors of the physics building at Harvard University showed that the clock on the ground floor ran more slowly showed that the clock on the ground floor ran more slowly than the one on the top floor confirming Einstein’s predictionthan the one on the top floor confirming Einstein’s prediction

It was further confirmed in 1976 by the measurements of time It was further confirmed in 1976 by the measurements of time delays experienced by radio signals sent by the Viking lander delays experienced by radio signals sent by the Viking lander on Mars as they passed near the Sun on Mars as they passed near the Sun

The delays were The delays were also caused by also caused by the curving of the curving of spacetime near spacetime near the Sunthe Sun


Black-Hole FormationBlack-Hole Formation


Ultra-strong GravityUltra-strong GravityAs a massive star collapses, the gravity on its surface As a massive star collapses, the gravity on its surface increases and therefore, according to general relativity, the increases and therefore, according to general relativity, the spacetime around the star becomes more and more curvedspacetime around the star becomes more and more curved

In other words, the curvature of the spacetime increasesIn other words, the curvature of the spacetime increases

As a result, when the star has shrunk down to a sufficiently As a result, when the star has shrunk down to a sufficiently small size (small size (just a little larger than a black-hole), only light just a little larger than a black-hole), only light beams sent out perpendicularly to its beams sent out perpendicularly to its surface could escapesurface could escape

Other light beams and objects sent outward Other light beams and objects sent outward could no longer escape, following paths that could no longer escape, following paths that curve back to the surfacecurve back to the surface

If the collapsing star shrinks just a little If the collapsing star shrinks just a little more, nothing will be able to escape and more, nothing will be able to escape and the star will become a the star will become a black holeblack hole

Since not even light can escape, the object Since not even light can escape, the object appears blackappears blackThe black hole’s size defines its The black hole’s size defines its event horizonevent horizon


““Event Horizon”Event Horizon”


Escape Velocity: Rocket Escape Velocity: Rocket Analogy Analogy


Escape VelocitiesEscape VelocitiesWhite dwarfs and neutron stars have very large White dwarfs and neutron stars have very large surface escape velocities because they have roughly surface escape velocities because they have roughly the mass of the Sun packed into an incredibly small the mass of the Sun packed into an incredibly small volumevolumeA solar-mass white dwarf has a radius of only 8,800 A solar-mass white dwarf has a radius of only 8,800 kilometerskilometers

Its surface escape velocity is about 5,500 km/sIts surface escape velocity is about 5,500 km/s

A solar-mass neutron star would have a radius of just A solar-mass neutron star would have a radius of just 17 km, its surface escape velocity would be an 17 km, its surface escape velocity would be an incredible 125,000 km/s! incredible 125,000 km/s! Real neutron stars have masses above 1.4 solar Real neutron stars have masses above 1.4 solar masses and smaller radii, so their escape velocities masses and smaller radii, so their escape velocities are even larger!are even larger!


Event HorizonEvent HorizonA black hole probably has no surfaceA black hole probably has no surfaceAstronomers use the distance at which the Astronomers use the distance at which the escape velocity equals the speed of light for escape velocity equals the speed of light for the size of the black holethe size of the black holeThis distance defines a surface called the This distance defines a surface called the event horizonevent horizon because because nono messages (via messages (via electromagnetic radiation or anything else) of electromagnetic radiation or anything else) of events happening within that distance of the events happening within that distance of the point mass can make it to the outsidepoint mass can make it to the outsideThe region within the event horizon thus The region within the event horizon thus appears blackappears black


Schwarzschild RadiusSchwarzschild RadiusWithin the event horizon space is so curved Within the event horizon space is so curved that any light emitted is bent back to the point that any light emitted is bent back to the point massmassKarl Schwarzschild was the physicist who Karl Schwarzschild was the physicist who derived the first exact solution to Einstein’s derived the first exact solution to Einstein’s equations of general relativityequations of general relativitySchwarzschild found that the light rays within a Schwarzschild found that the light rays within a certain distance of the point mass would be certain distance of the point mass would be bent back to the point massbent back to the point massThis distance is the same as the radius of the This distance is the same as the radius of the event horizonevent horizon, and is sometimes called the , and is sometimes called the Schwarzschild radiusSchwarzschild radius

2222AST 2010: Chapter 23AST 2010: Chapter 2319 April 200519 April 2005

What Would It Feel to Fall into a Black Hole?


Falling into a Black Hole (1)Falling into a Black Hole (1)According to theory, falling toward a black hole would not be a According to theory, falling toward a black hole would not be a pleasant experience…pleasant experience…

Falling feet-first, your body would be scrunched sideways and Falling feet-first, your body would be scrunched sideways and stretched along the length of your body by the tidal forces of stretched along the length of your body by the tidal forces of the black holethe black hole

Your body would look like a spaghetti noodle!Your body would look like a spaghetti noodle!

Stretching happens because your feet would be pulled much Stretching happens because your feet would be pulled much more strongly than your headmore strongly than your head

Sideways scrunching happens because all points of your body Sideways scrunching happens because all points of your body would be pulled toward the center of the black holewould be pulled toward the center of the black hole

Your shoulders would be squeezed closer together as you fell closer to Your shoulders would be squeezed closer together as you fell closer to the center of the black holethe center of the black hole

Tidal stretching/squeezing of anything falling into a black hole Tidal stretching/squeezing of anything falling into a black hole is conveniently forgotten in Hollywood moviesis conveniently forgotten in Hollywood movies


Falling into a Black Hole (2)Falling into a Black Hole (2)A friend watching you as you enter a black A friend watching you as you enter a black hole would see your clock run slower and hole would see your clock run slower and slower (than his) as you approached the event slower (than his) as you approached the event horizonhorizon

This is the effect of This is the effect of time dilationtime dilation

Your friend would see you take an infinite Your friend would see you take an infinite amount of time to cross the event horizonamount of time to cross the event horizon

Time would appear to him to stand stillTime would appear to him to stand still

However, in your reference frame your clock However, in your reference frame your clock would run forward normally and you would would run forward normally and you would reach the center very soon…reach the center very soon…

……a once-in-a-lifetime experiencea once-in-a-lifetime experience


Falling into a Black Hole (3) Falling into a Black Hole (3) If you reported back the progress of your If you reported back the progress of your journey into the black hole using photons with journey into the black hole using photons with very short wavelengths (very high very short wavelengths (very high frequencies), your friend would have to tune to frequencies), your friend would have to tune to progressively longer wavelengths (lower progressively longer wavelengths (lower frequencies) as you approached the event frequencies) as you approached the event horizonhorizon

This is the effect of This is the effect of gravitational redshift gravitational redshift

Eventually, the photons would be stretched to Eventually, the photons would be stretched to infinitely long wavelengthsinfinitely long wavelengths


Detecting Black Holes (1)Detecting Black Holes (1)Since, according to theory, black holes (their event Since, according to theory, black holes (their event horizons) are only several miles across and horizons) are only several miles across and completely black, how do we go about finding them?completely black, how do we go about finding them?Indirect methods must be used!Indirect methods must be used!

Their presence may be detected from their effects on Their presence may be detected from their effects on surrounding material and stars surrounding material and stars

A binary star system may have a black hole as one A binary star system may have a black hole as one of its membersof its members

The behavior of the visible companion may reveal whether The behavior of the visible companion may reveal whether or not the other is a black holeor not the other is a black holeIf sufficient data about the system is collected, Kepler’s If sufficient data about the system is collected, Kepler’s laws can be used to deduce the invisible object’s mass laws can be used to deduce the invisible object’s mass

If it is too big for a neutron star or a white dwarf, then it is likely a If it is too big for a neutron star or a white dwarf, then it is likely a black hole! black hole!


Views of a Possible Black Views of a Possible Black Hole Hole

far away up close


Detecting Black Holes (2)Detecting Black Holes (2)Measuring the masses of all of the binary systems in Measuring the masses of all of the binary systems in the Milky Way Galaxy would take much too long a the Milky Way Galaxy would take much too long a timetime

It is estimated that there are over a 100 billion binary It is estimated that there are over a 100 billion binary systems in the Galaxy!systems in the Galaxy!

Even if it took you just one second to somehow measure a Even if it took you just one second to somehow measure a binary's total mass and subtract out one star's mass, it binary's total mass and subtract out one star's mass, it would take you over 3,000 years to complete your surveywould take you over 3,000 years to complete your survey

How could you quickly hone on the binary systems How could you quickly hone on the binary systems that might have black holes? that might have black holes?

Fortunately, black holes can advertise their presence Fortunately, black holes can advertise their presence loud and clear with the X-ray emission associated loud and clear with the X-ray emission associated with themwith them


X-Ray EmissionX-Ray EmissionA visible star in a binary system loses some of its gas to its A visible star in a binary system loses some of its gas to its black-hole companionblack-hole companion

The gas material forms an accretion disk as it spirals onto the The gas material forms an accretion disk as it spirals onto the black holeblack hole

Gas particles in the disk rub against each and heat up from Gas particles in the disk rub against each and heat up from friction friction

As the particles whirl closer to the event horizon, the friction As the particles whirl closer to the event horizon, the friction can heat them up to 100 million kelvins, which is hot enough can heat them up to 100 million kelvins, which is hot enough for emission of X-raysfor emission of X-rays

Since X-ray sources in the Galaxy are rare, if you find an X-Since X-ray sources in the Galaxy are rare, if you find an X-ray source, then you know something strange is happening ray source, then you know something strange is happening with the objectwith the object

If the unseen companion is very small, then the X-ray brightness of the If the unseen companion is very small, then the X-ray brightness of the disk will be able to change rapidlydisk will be able to change rapidly


Accretion from a Binary Accretion from a Binary PartnerPartner


X-Ray X-Ray EmissionEmission

Visible Star

Gas pulled off

black hole

accretion disk

Gas temperature increases closer to BH. Gas near BH emits x-rays.Animation of black hole in binary star system


Chandra X-ray Chandra X-ray ObservatoryObservatory

It is one of NASA's great It is one of NASA's great observatoriesobservatories

launched by Space Shuttle launched by Space Shuttle Columbia on July 23, 1999Columbia on July 23, 1999

It detects/images X-ray It detects/images X-ray sources that are billions of sources that are billions of LY away LY awayChandra’s mirrors are the Chandra’s mirrors are the largest, most precisely largest, most precisely shaped and aligned, and smoothest mirrors ever constructedshaped and aligned, and smoothest mirrors ever constructedIt produces images 25 times sharper than the best previous X-It produces images 25 times sharper than the best previous X-ray telescoperay telescope

This focusing power is equivalent to the ability to read a newspaper at This focusing power is equivalent to the ability to read a newspaper at a distance of half a milea distance of half a mileChandra's improved sensitivity is making possible more detailed Chandra's improved sensitivity is making possible more detailed studies of black holes, supernovae, and other exotic objectsstudies of black holes, supernovae, and other exotic objects


Black-Hole CandidatesBlack-Hole CandidatesSeveral black-hole candidates have been Several black-hole candidates have been foundfound

Examples include Examples include Cygnus X-1 and V404 Cygni in the constellation of Cygnus X-1 and V404 Cygni in the constellation of Cygnus Cygnus

LMC X-3 in the constellation DoradoLMC X-3 in the constellation Dorado

V616 Mon in the Monocerotis constellationV616 Mon in the Monocerotis constellation

J1655-40 in ScorpiusJ1655-40 in Scorpius

and the closest, V4641 Sgr in Sagittarius, is about and the closest, V4641 Sgr in Sagittarius, is about 1600 light years away1600 light years away


Some Black-Hole Candidates in Binary Some Black-Hole Candidates in Binary Star SystemsStar Systems


Chandra's X-Ray Images of Chandra's X-Ray Images of Black HolesBlack Holes

This This moviemovie is a sequence of X-ray images of deep is a sequence of X-ray images of deep space taken by Chandra space taken by Chandra

The black holes are first marked, and then the view The black holes are first marked, and then the view zooms onto one pair of particularly close black holes, zooms onto one pair of particularly close black holes, known as SMG 123616.1+621513known as SMG 123616.1+621513

Astronomers believe that these black holes and their Astronomers believe that these black holes and their galaxies are orbiting each other and will eventually galaxies are orbiting each other and will eventually mergemerge

The movie ends by showing an The movie ends by showing an animationanimation of this of this scenarioscenario


Black Hole in Center of Milky Black Hole in Center of Milky WayWay

Astronomers believe that super-massive black-holes may Astronomers believe that super-massive black-holes may lie in the central regions of large galaxieslie in the central regions of large galaxies

These regions may serve as “feeding grounds” for black These regions may serve as “feeding grounds” for black holes that form therein holes that form therein

A black hole can grow in mass A black hole can grow in mass and size by “eating” the and size by “eating” the surrounding matter, such as surrounding matter, such as dust, asteroids, other stars, or dust, asteroids, other stars, or even other black holes even other black holes

The central region of our The central region of our Galaxy is thought to harbor Galaxy is thought to harbor a super-massive black-hole a super-massive black-hole with a mass of around 3.6 with a mass of around 3.6 million million MMSun Sun


Stellar QuestionStellar QuestionWhat would happen to the Earth’s orbit if the What would happen to the Earth’s orbit if the Sun were suddenly replaced by a black hole Sun were suddenly replaced by a black hole with the same mass as the Sun?with the same mass as the Sun?


Hollywood and RealityHollywood and RealityBlack holes are portrayed in TV and films as cosmic Black holes are portrayed in TV and films as cosmic vacuum cleaners, sucking up everything around vacuum cleaners, sucking up everything around themthem

or as tunnels from one universe to anotheror as tunnels from one universe to another

Black holes are dangerous only if something gets too Black holes are dangerous only if something gets too close to themclose to them

Because all of their mass is compressed to a point, it is Because all of their mass is compressed to a point, it is possible to get very close where the gravity gets very large possible to get very close where the gravity gets very large

Objects far enough away will not sense anything Objects far enough away will not sense anything unusualunusual

If the Sun were replaced by a black hole of the same mass, If the Sun were replaced by a black hole of the same mass, the orbits of the planets would remain unchangedthe orbits of the planets would remain unchangedIt would however be darker and colderIt would however be darker and colder

19 April 2005 AST 2010: Chapter 23 1 Black Holes & Curved Spacetime.

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Transcript of 19 April 2005 AST 2010: Chapter 23 1 Black Holes & Curved Spacetime.