A Review of the N-bound and the Maximal Mass Conjectures Using NUT-Charged dS Spacetimes

TL;DR

This paper reviews the N-bound and maximal mass conjectures in de Sitter spacetimes, demonstrating their limitations through examples involving NUT charge and providing insights into gravitational thermodynamics in these contexts.

Contribution

It introduces a generalized thermodynamic framework for asymptotically de Sitter spacetimes and shows that the N-bound and maximal mass conjectures can be violated in NUT-charged cases.

Findings

N-bound and maximal mass conjectures are not universally valid.

Explicit examples show violations of these conjectures in NUT-charged spacetimes.

Gravitational thermodynamics can be extended to include NUT charge in de Sitter spaces.

Abstract

The proposed dS/CFT correspondence remains an intriguing paradigm in the context of string theory. Recently it has motivated two interesting conjectures: the entropic N-bound and the maximal mass conjecture. The former states that there is an upper bound to the entropy in asymptotically de Sitter spacetimes, given by the entropy of pure de Sitter space. The latter states that any asymptotically de Sitter spacetime cannot have a mass larger than the pure de Sitter case without inducing a cosmological singularity. Here we review the status of these conjectures and demonstrate their limitation. We first describe a generalization of gravitational thermodynamics to asymptotically de Sitter spacetimes, and show how to compute conserved quantities and gravitational entropy using this formalism. From this we proceed to a discussion of the N-bound and maximal mass conjectures. We then illustrate that these conjectures are not satisfied for certain asymptotically de Sitter spacetimes with NUT charge. We close with a presentation of explicit examples in various spacetime dimensionalities.