On the quantum width of a black hole horizon

with a Planck scale cut-off. However, Sorkin has given a Newtonian argument for 3+1 Schwarzschild black holes to the effect that fluctuations of such modes provide the horizon with a non-zero quantum mechanical width. This width then effectively enforces a cut-off at much larger distances so that the entropy of the thermal atmosphere is negligible in comparison with

A/4G

for large black holes. We generalize and improve this result by giving a relativistic argument valid for any spherical black hole in any dimension. The result is again a cut-off

L_c

at a geometric mean of the Planck scale and the black hole radius: in particular,

L_c^d \sim \frac{R}{T_H} \ell_p^{d-2}

. With this cut-off, the entropy of the thermal atmosphere is again parametrically small in comparison with the Bekenstein-Hawking entropy of the black hole. The effect of a large number

N

of fundamental fields and the discrepancies from naive predictions of a stretched horizon model are also discussed.

talk: Dubrovnik 2003/09/04
black hole: horizon
entropy
horizon: width
black hole: Schwarzschild
horizon: fluctuation

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Figures(0)

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