Production and decay of evolving horizons

TL;DR

This paper presents a simple, spherically symmetric model for evolving black hole horizons interacting with matter and radiation, deriving straightforward formulae for horizon dynamics and thermodynamics applicable to astrophysical and theoretical contexts.

Contribution

It introduces a simplified, spherically symmetric framework for analyzing dynamic horizons, providing clear formulae for their growth, shrinkage, and thermodynamic properties in evolving black hole scenarios.

Findings

Derived simple expressions for surface gravity on evolving horizons.

Established first and second laws of black hole thermodynamics in a dynamic setting.

Related evolving horizons to various existing horizon concepts like apparent and trapping horizons.

Abstract

We consider a simple physical model for an evolving horizon that is strongly interacting with its environment, exchanging arbitrarily large quantities of matter with its environment in the form of both infalling material and outgoing Hawking radiation. We permit fluxes of both lightlike and timelike particles to cross the horizon, and ask how the horizon grows and shrinks in response to such flows. We place a premium on providing a clear and straightforward exposition with simple formulae. To be able to handle such a highly dynamical situation in a simple manner we make one significant physical restriction, that of spherical symmetry, and two technical mathematical restrictions: (1) We choose to slice the spacetime in such a way that the space-time foliations (and hence the horizons) are always spherically symmetric. (2) Furthermore we adopt Painleve-Gullstrand coordinates (which are well suited to the problem because they are nonsingular at the horizon) in order to simplify the relevant calculations. We find particularly simple forms for surface gravity, and for the first and second law of black hole thermodynamics, in this general evolving horizon situation. Furthermore we relate our results to Hawking's apparent horizon, Ashtekar et al's isolated and dynamical horizons, and Hayward's trapping horizons. The evolving black hole model discussed here will be of interest, both from an astrophysical viewpoint in terms of discussing growing black holes, and from a purely theoretical viewpoint in discussing black hole evaporation via Hawking radiation.