Surface gravity of compact non-degenerate horizons under the dominant energy condition

Abstract

We prove that under the dominant energy condition any non-degenerate smooth compact totally geodesic horizon admits a smooth tangent vector field of constant non-zero surface gravity. This result generalizes previous work by Isenberg and Moncrief, and by Bustamante and Reiris to the non-vacuum case, the vacuum case being given a largely independent proof. Moreover, we prove that any such achronal non-degenerate horizon is actually a Cauchy horizon bounded on one side by a chronology violating region.

Latex, 37 pages, 2 figures. v2: added appendix and one figure, expanded introduction

References in corpus (5)

• Symmetries of Higher Dimensional Black Holes
• Non-imprisonment conditions on spacetime
• Completeness of Cauchy horizon generators
• Yet another proof of Hawking and Ellis's Lemma 8.5.5
• The asymptotic expansion of the spacetime metric at the event horizon

Cited by in corpus (3)

• Analyticity of quasinormal modes in the Kerr and Kerr-de Sitter spacetimes
• Horizon classification via Riemannian flows
• Regularity and temperature of stationary black hole event horizons