Black Holes in de Sitter Space: Masses, Energies and Entropy Bounds

TL;DR

This paper investigates the thermodynamic properties and entropy bounds of black hole and cosmological horizons in de Sitter space using the Isolated Horizons formalism, revealing distinctions between mass and energy concepts.

Contribution

It introduces a detailed analysis of horizon energies and masses in de Sitter space, proposing new entropy bounds and comparing them with existing cosmological entropy limits.

Findings

Horizon energy can be zero while horizon mass remains finite in de Sitter space.

Derived generalized Bekenstein entropy bounds for horizons in de Sitter spacetime.

Compared thermodynamic results with Euclidean Hamiltonian methods.

Abstract

In this paper we consider spacetimes in vacuum general relativity --possibly coupled to a scalar field-- with a positive cosmological constant $\Lambda$. We employ the Isolated Horizons (IH) formalism where the boundary conditions imposed are that of two horizons, one of black hole type and the other, serving as outer boundary, a cosmological horizon. As particular cases, we consider the Schwarzschild-de Sitter spacetime, in both 2+1 and 3+1 dimensions. Within the IH formalism, it is useful to define two different notions of energy for the cosmological horizon, namely, the "mass" and the "energy". Empty de Sitter space provides an striking example of such distinction: its horizon energy is zero but the horizon mass takes a finite value given by $\pi/(2\sqrt\Lambda)$. For both horizons we study their thermodynamic properties, compare our results with those of Euclidean Hamiltonian methods and construct some generalized Bekenstein entropy bounds. We discuss these new entropy bounds and compare them with some recently proposed entropy bounds in the cosmological setting.