Statistical effects and the black-hole–D-brane correspondence

Abstract

The horizon area and curvature of three-charge BPS black strings are studied in the D-brane ensemble for the stationary black string. The charge distributions along the string are used to translate the classical expressions for the horizon area and curvature of BPS black strings with waves into operators on the D-brane Hilbert space. Despite the fact that any 'wavy' black string has smaller horizon area and divergent curvature, the typical values of the horizon area and effects of the horizon curvature in the D-brane ensemble deviate negligibly from those of the original stationary black string in the limit of large integer charges. Whether this holds in general will depend on certain properties of the quantum bound states.

The Bekenstein formula and string theory (N-brane theory)

“…Entropy of a more general BPS six dimensional black string with has also been studied from the string theory perspective in [99,100,101,102,103]. In these works, left-moving waves on the string [104] are allowed to have large amplitudes.…”

Black string entropy from anomalous D-brane couplings

“…This leads to an intriguing symmetry between interchange of the two intersecting D-branes and hence of the interior and exterior regions of the black hole. 3 We shall argue that this new interpretation leads to the explanation of the discrepancy raised in the black hole/D-brane correspondence [6]. Indeed, this new picture leads us to consider both superobserver's and outside observer's points of view and we will show that, for an outsider observer, this interpretation effectively perturbs the classical extremal black string solution to the near-extremal case.…”

“…from the area of the stationary black hole [6]. Therefore for large winding number Q 1 Q 5 , the two areas can match.…”

“…the Hilbert space of both exterior and interior regions is relevant). A natural way to understand the black hole/D-brane correspondence is to identify a quantum area operator on D-brane Hilbert space whose classical limit yields the horizon area of the extremal black hole in N = 8 supergravity [6]. The five-dimensional black hole can be viewed as a six-dimensional black string which winds around a compact internal circle.…”

Singularities in wavy strings

“…To simplify the analysis, I show that the part of the spacetime (2.9) traversed by small infalling observers can be approximated by a plane wave metric. The approximation of the metric near the horizon was also discussed in [10].…”