Semiclassical (QFT) and Quantum (String) anti - de Sitter Regimes: New Results

TL;DR

This paper explores the quantum string entropy in Anti de Sitter space, revealing no phase transition at the string temperature and deriving new bounds on black hole entropy in this regime.

Contribution

It provides a detailed computation of quantum string entropy in AdS space, showing the absence of phase transitions and introducing new bounds on black hole entropy in the quantum regime.

Findings

No phase transition at the string temperature in AdS space.

Quantum string entropy differs significantly from Bekenstein-Hawking entropy at high H.

New bounds on black hole entropy in the AdS string regime.

Abstract

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states of mass m in Anti de Sitter space-time. For high m, (high Hm -->c/\alpha'), no phase transition occurs at the Anti de Sitter string temperature T_{s} which is higher than the flat space (Hagedorn) temperature t_{s}. (the Hubble constant H acts as producing a smaller string constant and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti de Sitter temperature scale . We compute the quantum string emission by a black hole in Anti de Sitter space-time (bhAdS). In the early evaporation stage, it shows the QFT Hawking emission with temperature T_{sem~bhAdS}, (semiclassical regime). For T_{sem~bhAdS}--> T_{s}, it exhibits a phase transition into a Anti de Sitter string state. New string bounds on the black hole emerge in the bhAdS string regime. We find a new formula for the full (quantum regime included) Anti de Sitter entropy S_{sem}, as a function of the usual Bekenstein-Hawking entropy S_{sem}^(0). For low H (semiclassical regime), S_{sem}^(0) is the leading term but for high H (quantum regime), no phase transition operates, in contrast to de Sitter space, and the entropy S_{sem} is very different from the Bekenstein-Hawking term S_{sem}^(0).