The Hawking paradox and the Bekenstein resolution in higher-dimensional spacetimes. (arXiv:1811.02574v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Hod_S/0/1/0/all/0/1">Shahar Hod</a>

The black-hole information puzzle has attracted much attention over the years

from both physicists and mathematicians. One of the most intriguing suggestions

to resolve the information paradox is due to Bekenstein, who has stressed the

fact that the low-energy part of the semi-classical black-hole emission

spectrum is partly blocked by the curvature potential that surrounds the black

hole. As explicitly shown by Bekenstein, this fact implies that the grey-body

emission spectrum of a (3+1)-dimensional black hole is considerably less

entropic than the corresponding radiation spectrum of a perfectly thermal

black-body emitter. Using standard ideas from quantum information theory, it

was shown by Bekenstein that, in principle, the filtered Hawking radiation

emitted by a (3+1)-dimensional Schwarzschild black hole may carry with it a

substantial amount of information, the information which was suspected to be

lost. It is of physical interest to test the general validity of the

“information leak” scenario suggested by Bekenstein as a possible resolution to

the Hawking information puzzle. In the present paper we analyze the

semi-classical entropy emission properties of higher-dimensional black holes.

In particular, we provide evidence that the characteristic Hawking quanta of

$(D+1)$-dimensional Schwarzschild black holes in the large $Dgg1$ regime are

almost unaffected by the spacetime curvature outside the black-hole horizon.

This fact implies that, in the large-$D$ regime, the Hawking black-hole

radiation spectra are almost purely thermal, thus suggesting that the emitted

quanta cannot carry the amount of information which is required in order to

resolve the information paradox. Our analysis therefore suggests that the

elegant information leak scenario suggested by Bekenstein cannot provide a

generic resolution to the intriguing Hawking information paradox.

The black-hole information puzzle has attracted much attention over the years

from both physicists and mathematicians. One of the most intriguing suggestions

to resolve the information paradox is due to Bekenstein, who has stressed the

fact that the low-energy part of the semi-classical black-hole emission

spectrum is partly blocked by the curvature potential that surrounds the black

hole. As explicitly shown by Bekenstein, this fact implies that the grey-body

emission spectrum of a (3+1)-dimensional black hole is considerably less

entropic than the corresponding radiation spectrum of a perfectly thermal

black-body emitter. Using standard ideas from quantum information theory, it

was shown by Bekenstein that, in principle, the filtered Hawking radiation

emitted by a (3+1)-dimensional Schwarzschild black hole may carry with it a

substantial amount of information, the information which was suspected to be

lost. It is of physical interest to test the general validity of the

“information leak” scenario suggested by Bekenstein as a possible resolution to

the Hawking information puzzle. In the present paper we analyze the

semi-classical entropy emission properties of higher-dimensional black holes.

In particular, we provide evidence that the characteristic Hawking quanta of

$(D+1)$-dimensional Schwarzschild black holes in the large $Dgg1$ regime are

almost unaffected by the spacetime curvature outside the black-hole horizon.

This fact implies that, in the large-$D$ regime, the Hawking black-hole

radiation spectra are almost purely thermal, thus suggesting that the emitted

quanta cannot carry the amount of information which is required in order to

resolve the information paradox. Our analysis therefore suggests that the

elegant information leak scenario suggested by Bekenstein cannot provide a

generic resolution to the intriguing Hawking information paradox.

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