Foliation dependence of black hole apparent horizons in spherical symmetry

TL;DR

This paper investigates the foliation dependence of apparent horizons in spherical symmetry, proposing a physically meaningful approach using spherically symmetric slicings and analyzing implications for black hole properties.

Contribution

It introduces a method to address foliation dependence in spherical symmetry using the Hawking quasilocal mass and discusses properties of common slicings like comoving and Kodama.

Findings

Apparent horizons are gauge-independent in spherically symmetric foliations.

Physical quantities like surface gravity depend on the choice of foliation.

The approach clarifies the physical interpretation of apparent horizons in spherical symmetry.

Abstract

Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation-dependent. We expose the problem and discuss possible solutions using the Hawking quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry the apparent horizons are gauge-independent in any spherically symmetric foliation but physical quantities associated with them, such as surface gravity and temperature, are not. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail.