Surface Gravity of Compact Non-degenerate Horizons Under the Dominant Energy Condition

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.

Automated summary

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