PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

Chapter 1
Introduction
Einstein proposed the general theory of relativity in 1915. Almost a decade after that Quantum
theory was formulated. Since then people have tried to formulate a quantum theory of gravity
which will unify the principle of general covariance with the principles of quantum mechanics.
String theory is the leading candidate for such a theory.
But what are the effects of quantum gravity ? We do not hope to see quantum gravity
effects in our daily life. We do not even hope to see it in the present day high energy particle
accelarators. So what is the way out? At present it seems that the only place to look for
quantum gravity effects is the sky.
Black Holes are classical solutions of the equations of General Theory of Relativity. They
have the characteristic feature that the space-time curvature blows up at a point which is called
the singularity. It is almost an experimental fact that at the center of every galaxy there is a
black hole. It is believed that a black hole produced as a result of gravitaional collapse will
always be surrouned by a horizon of finite area which allows inflow of matter and radiation
but nothing can come out of it. Black holes have many things in common with an ordinary
thermodynamic system. For example the area of the black hole horizon behaves in many ways
like the entropy of a thermodynamic system. For example if two black holes collide and form
a single black hole then the area of the horizon of the new black hole will be greater than the
sum of the horizon areas of the parent black holes. This, along with many other indications,
led Bekenstein to conjecture that black hole carries entropy proportional to its horizon area.
Immediately after that Bardeen, Carter and Hawking proposed the four laws of black hole
thermodynamics. This proved, to some extent, that a black hole is a thermodynamic system
whick has entropy and has a finite temparature. But this immediately led to the following
puzzle. We know that a body at finite temparature emits radiation. In the case of black
hole no radiation can come out of it. Stephen Hawking resolved the puzzle by showing that
quantum mechanically black holes can emit and the spectrum matches exactly with that of
a blackbody kept at the same temparature as the black hole. His calculation also fixed the
proportionality constant to be 1/4, for a specific choice of units.This proved beyond doubt
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