Abstract
The black-hole information puzzle, first discussed by Hawking four decades ago, 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 gray-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. To this end, 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 D≫1 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 (non-thermal) information which is required in order to resolve the information paradox. Our analysis therefore suggests that the elegant information leak scenario suggested by Bekenstein, which is based on the effective gray-body (rather than a black-body) nature of the black-hole emission spectra, cannot provide a generic resolution to the intriguing Hawking information paradox.
Highlights
The black-hole information puzzle, first discussed by Hawking four decades ago, has attracted much attention over the years from both physicists and mathematicians
The characteristic relation (1) reflects the physically interesting fact that, due to the effective curvature potential of the black-hole spacetime, the low frequency part of the Hawking black-hole emission spectra is characterized by occupation numbers which are smaller than the corresponding occupation numbers of a purely thermal black-body radiation [3]
In his physically intriguing work [3], Bekenstein has stressed the fact that the black-hole emission spectrum is partly blocked by the effective curvature potential [see Eq (10)] that surrounds the emitting black hole
Summary
The black-hole evaporation phenomenon, first predicted by Hawking [1] more than four decades ago, imposes a great challenge to our understanding of the interplay between gravity and quantum theory. Hawking’s semi-classical analysis [1] asserts that black holes which were formed from the gravitational collapse of pure quantum states will emit thermally distributed radiation and eventually evolve into mixed thermal states This intriguing physical scenario is in sharp contradiction with the fundamental quantum mechanical principle of unitary temporal evolution, which asserts that pure quantum states should always remain pure as they evolve in time [2]. According to Hawking’s semi-classical analysis [1], the information hidden in the intermediate black-hole state about the initial quantum state of the collapsed matter is lost forever with the complete thermal evaporation of the black hole This physically intriguing scenario is known as the Hawking black-hole information puzzle
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