Entropy and Mass Bounds of Kerr-de Sitter Spacetimes

TL;DR

This paper analyzes Kerr-de Sitter spacetimes, evaluating their mass, entropy, and angular momentum, and tests various conjectures about their properties, revealing insights into their thermodynamics and the behavior of the c-function.

Contribution

It provides a detailed evaluation of mass, angular momentum, and entropy in Kerr-de Sitter spacetimes and tests the maximal mass conjecture and its strengthening.

Findings

Entropy of Kerr-de Sitter is less than pure de Sitter, consistent with the entropic N-bound.

Maximal mass conjecture holds for Kerr-de Sitter with rotation.

The c-function is anisotropic but averages to a RG flow consistent with spacetime expansion.

Abstract

We consider Kerr-de Sitter spacetimes and evaluate their mass, angular momentum and entropy according to the boundary counterterm prescription. We provide a physicall interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr-de Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the entropic N-bound. Moreover, we show that maximal mass conjecture which states any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity is respected by asymptotically de Sitter spacetimes with rotation. We furthermore consider the possibility of strengthening the conjecture to state that any asymptotically dS spacetime will have mass greater than dS if and only if it has a cosmological singularity and find that Kerr-de Sitter spacetimes do not respect this stronger statement. We investigate the behavior of the c-function for the Kerr-de Sitter spacetimes and show that it is no longer isotropic. However an average of the c-function over the angular variables yields a renormalization group flow in agreement with the expansion of spacetime at future infinity.