07.01.2014 Views

PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

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 />

xiii

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!