General Laws of Black-Hole Dynamics

TL;DR

This paper introduces a comprehensive framework for defining black holes using trapping horizons, deriving laws analogous to thermodynamics, and establishing properties like area increase and surface gravity in a general setting.

Contribution

It provides a unified, geometric definition of black holes via trapping horizons and formulates their dynamic laws, extending classical concepts to more general, possibly non-stationary cases.

Findings

Future outer trapping horizons have non-decreasing area (second law).

A generalized surface gravity (zeroth law) is defined with an upper bound.

The area variation is related to trapping gravity and energy flux (first law).

Abstract

A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces of one of four non-degenerate types, described as future or past, and outer or inner. If the boundary of an inextendible trapped region is suitably regular, then it is a (possibly degenerate) trapping horizon. The future outer trapping horizon provides the definition of a black hole. Outer marginal surfaces have spherical or planar topology. Trapping horizons are null only in the instantaneously stationary case, and otherwise outer trapping horizons are spatial and inner trapping horizons are Lorentzian. Future outer trapping horizons have non-decreasing area form, constant only in the null case---the `second law'. A definition of the trapping gravity of an outer trapping horizon is given, generalizing surface gravity. The total trapping gravity of a compact outer marginal surface has an upper bound, attained if and only if the trapping gravity is constant---the `zeroth law'. The variation of the area form along an outer trapping horizon is determined by the trapping gravity and an energy flux---the `first law'.