  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.
