What Is the Connection Between Black Hole Entropy and the Holographic Principle?

[Edward Wij]

How exactly did Hawking compute that black hole entropy is 1/4 that of a Planck area and concluded about the holographic principle where information of a volume is located on the area of black hole? And if there was no holographic principle, how big should entropy of the black hole be with reference to Planck area (would it be say 1/8 or twice that of Planck area for example)? How is this computed?

What observational evidence is there for these? Do all observations still obey the holographic principle?

 

[mfb]

How exactly

Black Holes and Entropy
Bekenstein, Phys. Rev. D 7, 2333, abstract

Black hole explosions?
Hawking, Nature 248, 30 - 31 (01 March 1974), abstract

There is no observational evidence for hawking radiation from black holes at all - but that is not unexpected as the radiation is so weak. There are some experiments that see similar effects in other types of effective horizons (water waves, I think currents, and whatever).

 

[PeterDonis]

the holographic principle where information of a volume is located on the area of black hole?

Hawking didn't come up with this principle, and it is a separate concept from the computation of entropy in terms of the horizon area. See here:

http://en.wikipedia.org/wiki/Holographic_principle

if there was no holographic principle, how big should entropy of the black hole be with reference to Planck area (would it be say 1/8 or twice that of Planck area for example)?

The computation of the black hole entropy, as above, does not depend on the holographic principle; it is the same whether that principle is true or false.

 

[Chalnoth]

There is no observational evidence for hawking radiation from black holes at all - but that is not unexpected as the radiation is so weak. There are some experiments that see similar effects in other types of effective horizons (water waves, I think currents, and whatever).

Yes, the primary evidence for Hawking Radiation from black holes is that when we create a horizon in some other wave medium (such as sound waves in a fluid), we get Hawking radiation emitted from the horizon.

 

[Edward Wij]

Hawking didn't come up with this principle, and it is a separate concept from the computation of entropy in terms of the horizon area. See here:

http://en.wikipedia.org/wiki/Holographic_principle
The computation of the black hole entropy, as above, does not depend on the holographic principle; it is the same whether that principle is true or false.

Ok I realized now, but I wondered this (and caused of my initial confusion). Since Hawking was the first one to discover about the computation of entropy in the terms of the horizon area, how come he didn't conclude that all information of physical systems can be located in the area and not volume. How come it needs others (Susskind) to realize this?

 

[PeterDonis]

Since Hawking was the first one to discover about the computation of entropy in the terms of the horizon area, how come he didn't conclude that all information of physical systems can be located in the area and not volume. How come it needs others (Susskind) to realize this?

I couldn't say. Anyway, that's not a question of physics, it's a question of history and human psychology.