BLACK HOLES

Overview

Black holes are the densest, most massive singular objects in the

universe. Formed in one of three main processes, they exert so much

gravitational force that nothing - not even light - can escape their pull.

Since nothing can ever come out, it is called a hole. Since not even light

nor other electromagnetic radiation can escape, it is called a black hole.

Black Holes

A black hole can be formed in the manner described above, but

also in two other ways. The first is that if a star has more than nine solar

masses when it goes supernova, then it will collapse into a black hole.

The reason that a neutron star stops collapsing is the strong nuclear

force, the fundamental force that keeps the center of an atom from

collapsing.

However, once a star is this big, the gravitational force is so

strong that it overwhelms this force and collapses the atom completely.

Now there is nothing to hold back collapse, and it collapses into a point

(or, in theory, a ring) of infinite density.

Stephen Hawking proposed a third way a black hole could form,

theorizing that trillions were produced in the Big Bang with some still

existing today. This theory is not as widely accepted.

The infinite density of the black hole causes such a strong

gravitational well that not even light can escape from it. Since nothing

can ever come out, it is called a hole. Since not even light or other

electromagnetic radiation can escape, it is called a black hole.

A black hole's anatomy is pretty simple. The hole itself is known

as a singularity. This is the very center of the black hole, and is where the

mass of the original star (and all acquired matter) lies.

In a Kerr black hole (a black hole that assumes the star's core was

spinning and had a magnetic field when it collapsed), the singularity is

theorized to be ring-shaped. In a black hole that does not spin, the

singularity is a dimensionless point of infinite density.

Moving out from the center, the next part is the inner event

horizon. Between the inner event horizon and the singularity, space is

believed to be relatively normal - except for the fact that all objects are

drawn towards the singularity and cannot escape.

Next out is the outer event horizon. This marks the boundary at

which the escape velocity is greater than the speed of light, and all

known objects are drawn into the hole. This also marks the "outer edge"

of the black hole; we cannot see into it, for no form of known radiation

can escape the gravitational pull from this point inward.

The next part of the black hole is only present in a spinning black

hole. The ergosphere is a region of space where all particles are drawn in

a circular path that match the hole's rotation.

However, within the ergosphere, matter and energy can still

escape the hole's grasp. The outer edge of the ergosphere is called the

static limit. This is the distance that matter must maintain in order to

keep a stable orbit and not be trapped by the hole's rotation.

NOTE:

The only physical part of a black hole is the singularity. The other

parts mentioned are mathematical boundaries. There is no physical

barrier called an event horizon, but it marks the boundaries between

types of space under the influences of the singularity.

Other parts of a black hole are present only in "active" black

holes. The accretion disk is matter that has been trapped in orbit around

the black hole. It will gradually be pulled into the hole.

As it gets closer, its speed increases, and it also gains energy and

begins to emit light. This is the radiation that astronomers can use to

determine how much the black hole "weighs." By using the doppler

effect, astronomers can determine how fast the material is revolving

around the black hole, and thus can infer its mass.

Most black holes that have been found usually weigh several

million solar masses.

No black hole has actually been imaged in a telescope. Actually,

this is in itself impossible because, simply by definition, one cannot see

"nothing." A black hole can only be spotted by observing how the

material around it acts (inferred in the method in the previous paragraph).

Through this method, astronomers have observed many dozens of

black holes; they usually are found in the center of galaxies, and some

believe that every galaxy harbors a black hole in its center.

MATHEMATICAL

PROPERTIES OF BLACK

HOLES

A black hole is a theoretical entity predicted by the equations of

general relativity.

Black Holes from Relativity

Within months of Einstein's publication of general relativity in

1916, the physicist Karl Schwartzchild produced a solution to Einstein's

equation for a spherical mass (called the Schwartzchild metric) ... with

unexpected results.

The Schwarzschild radius (sometimes historically referred to as

the gravitational radius) is the distance from the center of an object such

that, if all the mass were compressed within that region, the escape speed

would equal the speed of light.

Once a stellar remnant collapses within this radius, light cannot

escape and the object is no longer visible.

The Schwarzschild radius is proportional to the mass with a

proportionality constant involving the gravitational constant and the

speed of light from the perspective of an observer at infinity and not in

motion relative to the black hole:

where;

rs is the Schwarzschild radius;

G is the gravitational constant;

m is the mass of the gravitating object;

c is the speed of light in vacuum.

The proportionality constant, 2G/c2, is approximately

1.48×10−27 m/kg, or 2.95 km/solar mass

An object of any density can be large enough to fall within its

own Schwarzschild radius,

where;

Vs is the volume of the object;

ρ is its density.

Vs α ρ-3/2

The gravitational constant, denoted G, is an empirical physical

constant involved in the calculation of the gravitational attraction

between objects with mass. It appears in Newton's law of universal

gravitation and in Einstein's theory of general relativity.

G = 6.67428x10-11m3kg-1s-2 = 6.67428x10-11N(m/kg)2

CLASSIFICATION BY

SCHWARZSCHILD RADIUS

Supermassive Black Hole

If one accumulates matter at normal density (1 g/cm3, for

example, the density of water) up to about 150,000,000 times the mass of

the Sun, such an accumulation will fall inside its own Schwarzschild

radius and thus it would be a supermassive black hole of 150,000,000

solar masses.

Stellar Black Hole

If one accumulates matter at nuclear density (the density of the

nucleus of an atom, about 1018 kg/m3; neutron stars also reach this

density), such an accumulation would fall within its own Schwarzschild

radius at about 3 solar masses and thus would be a stellar black hole.

CHANDRASEKHAR LIMIT

The Chandrasekhar limit is an upper bound on the mass of

bodies made from electron-degenerate matter, a dense form of matter

which consists of nuclei immersed in a gas of electrons.

The limit is the maximum nonrotating mass which can be

supported against gravitational collapse by electron degeneracy

pressure. It is named after the Indian astrophysicist Subrahmanyan

Chandrasekhar, and is commonly given as being about 1.4 solar

masses.

Computed values for the limit will vary depending on the

approximations used, the nuclear composition of the mass, and the

temperature.Chandrasekhar gives a value of:

Here, μe is the average molecular mass per electron, mH is the mass of the

hydrogen atom, and

is a constant connected with the solution to the Lane-

Emden equation. Numerically, this value is approximately

(2/μe)2 x2.85x1030 kg, or ;

1.43 (2/μe)2 M☉,

where

M☉=1.989·1030 kg is the standard solar mass.

is the Planck mass, MPl≈2.176·10−8 kg, the limit is of the

order of

Example: Calculate schwarzschild radius for the sun for the earth

for the mountain everest and for human.

(msun=1.98892x1030kg,mearth=5.9736x1024kg,meverest=3.041x1015kg,

mhuman=70kg )

Solution:

rs =(2*G*m)/c2 and

G=(6.67428x10-11N/(m/kg)2

For sun;

rs-sun=(2*6.67428x1011N/(m/kg)2*1.98892x1030kg)/(3x108)2 = 2949.9m

rs-earth=(2*6.67428x10-11N/(m/kg)2*5.9736x1024kg)/(3x108)2=8.85x10-3m

rs-evrs=(2*6.67428x10-11 N/(m/kg)2*3.041x1015kg)/(3x108)2 =4.51x10-12m

rs-human=(2*6.67428x10-11N/(m/kg)2*70kg)/(3x108)2 = 1.03x10-25m

N.FULYA ERCENGİZ