PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

Synopsis
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 believed that a black hole produced as a result of gravitational collapse will
always be surrounded by a horizon of finite area which allows inflow of matter and radiation
but nothing can come out of it. 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
which has entropy and has a finite temperature. But this immediately led to the following
puzzle. We know that a body at finite temperature 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
black body kept at the same temperature as the black hole. This proved beyond doubt that
black holes are thermodynamic objects and so we are allowed to ask all sorts of questions about
its ”constituents”.
The development so far depended only on General Theory of Relativity and Quantum
Field theory on Curved Spacetime. But none of them can answer the following question. It
is known that the entropy of a thermodynamic system is proportional to the logarithm of the
number of micro states accessible to the system. So what are the microstaes of a black hole?
According to the General Theory of Relativity if we specify the mass, charge and angular
momentum of a black hole then the solution is uniquely specified. So classically the entropy
vanishes and we need a theory other than General Theory of Relativity which can give us
information about the micro states of a black hole and its nature. String Theory is one such
candidate. It is a quantum theory of gravity and it can talk meaningfully and unambiguously
about black hole and its micro states.
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