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 tangent vector field of constant non-zero surface gravity. This result generalizes previous work by Isenberg and Moncrief, Bustamante Reiris to non-vacuum case, vacuum case being given largely independent proof. Moreover, we such achronal is actually Cauchy bounded on one side chronology violating region.