Finite black hole entropy and string theory

Abstract

An accelerating observer sees a thermal bath of radiation at the Hawking temperature which is proportional to the acceleration. Also, in string theory there is a Hagedorn temperature beyond which one cannot go without an in nite amount of energy. Several authors have shown that in the context of Hawking radiation a limiting temperature for string theory leads to a limiting acceleration, which for a black hole implies a minimum distance from the horizon for an observer to remain stationary. We argue that this e ectively introduces a cuto in Rindler space or the Schwarzschild geometry inside of which accelerations would exceed this maximum value. Furthermore, this natural cuto in turn allows one to de ne a nite entropy for Rindler space or a black hole as all divergences were occurring on the horizon. In all cases if a particular relationship exists between Newton's constant and the string tension then the entropy of the string modes agrees with the Bekenstein-Hawking formula.

Perturbative string thermodynamics near black hole horizons

“…It shows that higher genus amplitudes have in their dominating contribution only support close to the tip of the cigar. This implies that even higher loop corrections cannot modify the fact 34 In flat space, dependence of λ on the momentum quantum number is interpreted as a derivative interaction. In general, such a derivative is not diagonal in the basis ψ l .…”

“…34 This amplitude can now be rewritten as 17) where in the second line, one should focus on the most dominant mode of the thermal scalar (hence the approximation symbol). 35 Both of these equalities teach us something about the higher genus amplitudes.…”

“…[11,15,16,[30][31][32][33][34]. In general one expects higher worldsheet corrections to be neglible when considering the exterior of black holes.…”

Massive scalar particles in a modified Schwarzschild geometry

“…The existence of a MA would rid black hole entropy of ultraviolet divergencies [10], [11], and circumvent inconsistencies associated with the application of the point-like concept to relativistic quantum particles [12].…”

Maximal acceleration and radiative processes

“…MA also appears in the context of Weyl space [37][38][39][40] and of a geometrical analogue of Vigier's stochastic theory [41]. It is invoked as a tool to rid black hole entropy of ultraviolet divergences [42] and is at times regarded as a regularization procedure [43] that avoids the introduction of a fundamental length [44], thus preserving the continuity of space-time.…”