Entropy and Mass Bounds of Kerr-de Sitter Spacetimes

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.

13 pages, 3 figures, one figure added, typos corrected

References in corpus (6)

• The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes
• Rotating Black Holes in Higher Dimensions with a Cosmological Constant
• Breakdown of the Entropy/Area Relationship for NUT-charged Spacetimes
• Entropic N-bound and Maximal Mass Conjecture Violations in Four Dimensional Taub-Bolt(NUT)-dS Spacetimes
• Mass, Action and Entropy of Taub-Bolt-dS Spacetimes
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• Positive mass theorems for asymptotically de Sitter spacetimes
• Holography in Three-dimensional Kerr-de Sitter Space with a Gravitational Chern-Simons Term
• Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background
• On Black Ring with a Positive Cosmological Constant
• Quasinormal Modes and Hidden Conformal Symmetry of Warped dS${}_3$ Black Hole
• The definition of mass in asymptotically de Sitter space-times
• Einstein-Gauss-Bonnet black holes in de Sitter spacetime and the quasilocal formalism
• Entropy of higher-dimensional charged de Sitter black holes and phase transition
• Recent progress on the positive energy theorem
• Dual CFT on Nariai limit for Kerr-Sen-dS black holes
• Central Singularity of Three-Dimensional Kerr-de Sitter Black Holes