On the Thermodynamics of Goedel Black Holes

TL;DR

The paper investigates the thermodynamics of black holes in Gödel universes, highlighting an entropy upper bound $S$ that suggests a finite-dimensional holographic dual and a minimum temperature $T_{ ext{min}} = \frac{16 j}{3\sqrt{3}\pi}$, analogous to Hawking-Page physics. It analyzes the Schwarzschild-Gödel black hole embedded in Gödel space, deriving its horizon structure and thermodynamic quantities, and reveals substantial ambiguities in defining mass and charges due to nonstandard asymptotics and Chern-Simons terms; a Smarr-type relation and a first-law form $dE = T dS + \omega_H dJ$ can be formulated, but fixing the integration constants to match various limits does not uniquely determine the physical masses. The work suggests that embedding Gödel black holes in Gödel-AdS (with negative $\Lambda$) could regulate CTCs and yield a well-defined thermodynamic framework, motivating future studies of phase structure and holographic interpretations in this regulator regime.

Abstract

After a brief review of Goedel-type universes in string theory, we discuss some intriguing properties of black holes immersed in such backgrounds. Among these are the upper bound on the entropy that points towards a finite-dimensional Hilbert space of a holographically dual theory, and the minimum black hole temperature that is reminiscent of the Hawking-Page transition. Furthermore, we discuss several difficulties that are encountered when one tries to formulate a consistent thermodynamics of Goedel black holes, and point out how they may be circumvented.

Figures (2)

• Figure 1: Entropy $S$ of the Schwarz-schild-Gödel black hole as a function of the mass parameter.
• Figure 2: Temperature $T$ as a function of $m$.