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PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

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Synopsis<br />

Black Holes are classical solutions of the equations of General Theory of Relativity. They have<br />

the characteristic feature that the space-time curvature blows up at a point which is called the<br />

singularity. It is believed that a black hole produced as a result of gravitational collapse will<br />

always be surrounded by a horizon of finite area which allows inflow of matter and radiation<br />

but nothing can come out of it. The area of the black hole horizon behaves in many ways like<br />

the entropy of a thermodynamic system. For example if two black holes collide and form a<br />

single black hole then the area of the horizon of the new black hole will be greater than the<br />

sum of the horizon areas of the parent black holes. This, along with many other indications,<br />

led Bekenstein to conjecture that black hole carries entropy proportional to its horizon area.<br />

Immediately after that Bardeen, Carter and Hawking proposed the four laws of black hole<br />

thermodynamics. This proved, to some extent, that a black hole is a thermodynamic system<br />

which has entropy and has a finite temperature. But this immediately led to the following<br />

puzzle. We know that a body at finite temperature emits radiation. In the case of black<br />

hole no radiation can come out of it. Stephen Hawking resolved the puzzle by showing that<br />

quantum mechanically black holes can emit and the spectrum matches exactly with that of a<br />

black body kept at the same temperature as the black hole. This proved beyond doubt that<br />

black holes are thermodynamic objects and so we are allowed to ask all sorts of questions about<br />

its ”constituents”.<br />

The development so far depended only on General Theory of Relativity and Quantum<br />

Field theory on Curved Spacetime. But none of them can answer the following question. It<br />

is known that the entropy of a thermodynamic system is proportional to the logarithm of the<br />

number of micro states accessible to the system. So what are the microstaes of a black hole?<br />

According to the General Theory of Relativity if we specify the mass, charge and angular<br />

momentum of a black hole then the solution is uniquely specified. So classically the entropy<br />

vanishes and we need a theory other than General Theory of Relativity which can give us<br />

information about the micro states of a black hole and its nature. String Theory is one such<br />

candidate. It is a quantum theory of gravity and it can talk meaningfully and unambiguously<br />

about black hole and its micro states.<br />

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