## TyroCity

Physics XI Notes for Physics Notes

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# Black Hole

A black hole is a region of space in which the gravitational pull is so strong that nothing can escape. General relativity predicts that if a star of mass more than solar masses have 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 not outward. As a result, the object is dark i.e. black and hides from view a finite region of space.

The escape velocity,
shows that a body of mass M will act as a black hole if its radius R is 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:

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 a black hole. Any other body within a distance Rs 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 cannot see events occurring inside it. 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).

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; this effect is called time dilation. Actually, the observers would never see you due to horizon.

As you fell with your 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 your 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 cannot escape from a black hole, then how can we know about black holes? The answer is that any gas or dust near to the black tends to be pulled into an accretion disc that swirls around and into the black hole, rather like a whirl pool. The friction within the accretion disc’s material causes it to 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 x-rays. Astronomers look for these x-rays emitted before the material crosses the event horizon to signal the presence of a black hole.