  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 $D\gg1$ 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.
