Monday, June 25, 2007

Curved space and monsters

New paper!

A simple question: how many different black holes can there be with mass M? Conventional wisdom: of order exp(A), where A is the surface area of the hole and scales as M^2.

Using curved space, we construct objects of ADM mass M with far more than exp(A) microstates. These objects have pathological properties, but, as far as we can tell, can be produced via quantum tunneling from ordinary (non-pathological) initial data. Our results suggest that the relation between black hole entropy and the number of microstates of the hole is more subtle than perhaps previously appreciated.

Update! Rafael Sorkin was kind enough to inform us of his earlier related work with Wald and Zhang. We've added the following end-note to the paper.

Note added: After this work was completed we were informed of related results obtained by Sorkin, Wald and Zhang [25]. Those authors investigated monster-like objects as well as local extrema of the entropy S subject to an energy constraint, which correspond to static configurations and obey $A^{3/4}$ scaling. For example, in the case of a photon gas the local extrema satisfy the Tolman--Oppenheimer--Volkoff equation of hydrostatic equilibrium. In considering monster configurations, Sorkin et al. show that requiring a configuration to be no closer than a thermal wavelength $\lambda \sim \rho^{-1/4}$ from its Schwarzschild radius imposes the bound $S < A$. While this may be a reasonable criterion that must be satisfied for the assembly of an initial configuration, it does not seem to apply to states reached by quantum tunneling. From a global perspective configurations with $S > A^{3/4}$ are already black holes in the sense that the future of parts of the object does not include future null infinity.

Black hole entropy, curved space and monsters

Stephen D.H. Hsu, David Reeb

(Submitted on 21 Jun 2007)

We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than their area in Planck units. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter $S < A^{3/4}$. This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states.


Dave Bacon said...

Freaky, I read this post just as my playlist switched to the song "Monsters" by Band of Horses. Now there's an idea for an interesting MP3 player: one which observes what your surfing and adjusts your playlist.

Kea said...

Was your choice of the term monster a deliberate reference to moonshine, or not?

steve said...

No, that is an unfortunate coincidence. I say unfortunate because it's misleading and (as far as I know) there is no connection between our monsters and the monster group.

We just called them monsters because they have pathological properties. Note these configurations have so much entropy (number of possible states) that they can't be accommodated in any kind of holographic dual description.

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