Surface gravity of compact non-degenerate horizons under the dominant energy condition
arXiv:2108.04056 · doi:10.1007/s00220-022-04440-8
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.
arXiv commentLatex, 37 pages, 2 figures. v2: added appendix and one figure, expanded introduction
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