The Hidden horizon and black hole unitarity

Englert, Francois; Spindel, Philippe

doi:10.1007/JHEP12(2010)065

The Hidden horizon and black hole unitarity

Francois Englert
(
- Brussels U. and
- Intl. Solvay Inst., Brussels
)
,
Philippe Spindel
(
- U. Mons
)

Sep, 2010

30 pages

Published in:

JHEP 12 (2010) 065

e-Print:

1009.6190 [hep-th]

DOI:

10.1007/JHEP12(2010)065

Report number:

ULB-TH-10-35

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Abstract: (arXiv)

We motivate through a detailed analysis of the Hawking radiation in a Schwarzschild background a scheme in accordance with quantum unitarity. In this scheme the semi-classical approximation of the unitary quantum - horizonless - black hole S-matrix leads to the conventional description of the Hawking radiation from a classical black hole endowed with an event horizon. Unitarity is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing of generic out-states, in addition to the in-state, yields in asymptotic Minkowski space-time saddle-point contributions which are dominated by Planckian metric fluctuations when approaching the Schwarzschild radius. We argue that these prevent the corresponding macroscopic 'exclusive backgrounds' to develop an event horizon. However, if no out-state is selected, a distinct saddle-point geometry can be defined, in which Planckian fluctuations are tamed. Such 'inclusive background' presents an event horizon and constitutes a coarse-grained average over the aforementioned exclusive ones. The classical event horizon appears as a coarse-grained structure, sustaining the thermodynamic significance of the Bekenstein-Hawking entropy. This is reminiscent of the tentative fuzzball description of extremal black holes: the role of microstates is played here by a complete set of out-states. Although the computations of unitary amplitudes would require a detailed theory of quantum gravity, the proposed scheme itself, which appeals to the metric description of gravity only in the vicinity of stationary points, does not.

Note:

29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes 3 and 5)

Black Holes
Models of Quantum Gravity
black hole: Schwarzschild
space-time: Minkowski
radiation: Hawking
sphere: fuzzy
approximation: semiclassical
S-matrix: unitarity
black hole: horizon
metric: fluctuation

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