Black Holes//Gravity and Gravitation//General Relativity//Event Horizon//Schwarzschild Radius//Einstein's General Theory of Relativity

 Black Holes

General relativity predicts that if a star of mass more than three solar masses has completely burned its nuclear fuel, it should collapse into configuration known as black hole. The resulting object is independent of the properties of matter that produced it and is completely described by its mass and spin. The most striking feature of this object is the existence of a surface called horizon, which completely encloses the collapsed matter. The horizon is an ideal one way membrane, i.e. particles and light can go inward through the surface but no con go outward. As a result, the object is dark i.e. black and hides from view a finite region of space.
C= d or
Rs = 2 GM
The escape velocity, v =
R shows that a body of mass M will act as a black hole if its radius Ris less than or equal to a certain critical radius. Karl Schwarzschild in 1916, derived an expression for the critical velocity from Einstein's' general theory of relativity, known as Schwarzschild radius Rs.
This is given as 2 GM
Rs 2 GM c?
If a spherical, non-rotating body of mass M has a radius smaller than Rs, then nothing - not even light -can escape from the surface of the body. The body is then black hole. Any other body within a distance
R. from the centre of the black hole is trapped by the gravitational attraction of the black hole and cannot escape from it.
The surface of sphere with radius Rs surrounding a black hole is called event horizon. We can not see events occurring inside it and all that can be known about a black hole is its mass (from its gravitational force on other bodies), its electric charge (from electric forces on other charged bodies) and its angular momentum (as a rotating black hole tends to drag the space and everything in it e around with it).
At points far from a black hole, its gravitational effects are the same as those of any normal body having same mass. So, if the sun collapsed to form a black hole, the orbits of the planets would not be affected, but things get dramatically different close to the black hole. If you go inside the black-hole carrying a radio transmitter to send the signals to the outside observers, they would have to return their receiver continuously to lower and lower frequencies; this effect is called the gravitational red shift. Consistent with this shift, the outside observers would observe that the clock would appear to run more and more slowly, an effect called time dilation. Actually, the observers would never see you make it to the event horizon. As you fell with feet first into the black hole, the gravitational pull on your feet would be greater than that on your head. The differences in gravitational force on different parts of your body would be greater enough to stretch you along the direction towards the black hole and compress you perpendicular to it. These effects, called tidal forces, would rip you to atoms, and then rip your atoms apart, before you reached the event horizon.
Since light can not escape from a black hole, then how can we know about the black holes? The answer is that any gas or dust near to the black hole tends to be pulled into an accretion dise that swirls around and into the black hole, rather like a whirlpool. The friction within the accretion dise's material causes it lose mechanical energy and spiral into the black hole. As it moves inward, it is compressed together and this causes heating of the material, just as air compressed in a bicycle pump gets hotter.
Temperature in excess of 106 K can occur in the accretion disc so that the disc emits not just visible light, but x-rays also. Astronomers look for these x-rays emitted before the material crosses the event horizon to signal the presence of a black hole.