On the existence of sections with constant surface gravity on null hypersurfaces

TL;DR

This paper investigates null hypersurfaces in certain spacetimes, demonstrating the existence of sections with constant surface gravity, which complements prior studies on horizons with zero expansion.

Contribution

It introduces a natural class of null hypersurfaces with sections of constant surface gravity under the null convergence condition.

Findings

Existence of null sections with constant surface gravity in specific spacetimes

Complementary to previous work on horizons with zero expansion

Provides new insights into the structure of null hypersurfaces in general relativity

Abstract

We identify, in spacetimes satisfying the null convergence condition, a certain natural class of null hypersurfaces that admit null sections with constant surface gravity. Our work is meant to offer complementary results to previous work on null hypersurfaces of zero expansion arising from the study of Cauchy and black hole horizons in general relativity.