Bulk/Boundary Thermodynamic Equivalence, and the Bekenstein and Cosmic-Censorship Bounds for Rotating Charged AdS Black Holes

TL;DR

This paper demonstrates the thermodynamic equivalence between bulk and boundary quantities for rotating AdS black holes, establishes bounds like the Bekenstein and cosmic censorship bounds, and explores temperature and horizon area limits across dimensions.

Contribution

It clarifies the relationship between bulk and boundary thermodynamics, correcting previous misconceptions, and uncovers universal bounds related to black hole and cosmological horizons in various dimensions.

Findings

Bulk and boundary thermodynamic quantities satisfy the first law consistently.

Boundary quantities always satisfy an AdS-Bekenstein bound, not necessarily a Cardy-Verlinde formula.

Universal bounds on horizon areas and temperature limits are identified across dimensions.

Abstract

We show that one may pass from bulk to boundary thermodynamic quantities for rotating AdS black holes in arbitrary dimensions so that if the bulk quantities satisfy the first law of thermodynamics then so do the boundary CFT quantities. This corrects recent claims that boundary CFT quantities satisfying the first law may only be obtained using bulk quantities measured with respect to a certain frame rotating at infinity, and which therefore do not satisfy the first law. We show that the bulk black hole thermodynamic variables, or equivalently therefore the boundary CFT variables, do not always satisfy a Cardy-Verlinde type formula, but they do always satisfy an AdS-Bekenstein bound. The universal validity of the Bekenstein bound is a consequence of the more fundamental cosmic censorship bound, which we find to hold in all cases examined. We also find that at fixed entropy, the temperature of a rotating black hole is bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six or more dimensions. We find evidence for universal upper bounds for the area of cosmological event horizons and black-hole horizons in rotating black-hole spacetimes with a positive cosmological constant.