The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes

TL;DR

This paper investigates how the choice of spacetime slicing affects the properties of quasi-local horizons in Vaidya spacetimes, revealing that horizon areas depend on foliation but vary minimally for slowly evolving black holes.

Contribution

It provides a comparative analysis of different horizon definitions on non-spherical slicings in Vaidya spacetimes, including both numerical and analytical results.

Findings

Horizon location and area depend on foliation choice.

Area variation is small (~0.035%) for slowly evolving horizons.

Difference in area between horizons can be much larger than Planck area for large black holes.

Abstract

It is well known that quasi-local black hole horizons depend on the choice of a time coordinate in a spacetime. This has implications for notions such as the surface of the black hole and also on quasi-local physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on non-spherically symmetric slicings of Vaidya spacetimes. The spacetimes we investigate include both accreting and evaporating black holes. For some simple choices of the Vaidya mass function function corresponding to collapse of a hollow shell, we compare the area for the numerically found axisymmetric trapping horizons with the area of the spherically symmetric trapping horizon and event horizon. We find that as expected, both the location and area are dependent on the choice of foliation. However, the area variation is not large, of order $0.035\%$ for a slowly evolving horizon with $\dot{m}=0.02$. We also calculate analytically the difference in area between the spherically symmetric quasi-local horizon and event horizon for a slowly accreting black hole. We find that the difference can be many orders of magnitude larger than the Planck area for sufficiently large black holes.