Basics of Apparent Horizons in Black Hole Physics

TL;DR

This paper provides a detailed, pedagogical overview of apparent horizons in black hole physics, emphasizing their importance in numerical simulations and their relation to event horizons, especially in dynamic and spinning black holes.

Contribution

It offers a comprehensive explanation of apparent horizons, including the complex case of a slowly moving and spinning black hole, highlighting their practical significance in numerical relativity.

Findings

Clarifies the definition and properties of apparent horizons.

Demonstrates the application to a slowly moving and spinning black hole.

Highlights the importance in numerical simulations for stable black hole modeling.

Abstract

Event Horizon, a null hypersurface defining the boundary of the black hole region of a spacetime, is not particularly useful for evolving black holes since it is non-local in time. Instead, one uses the more tangible concept of Apparent Horizon for dynamical black holes out there in the sky that do all sorts of things: evolve, merge and feed on the environment. Event Horizon, being a gauge-independent, global property of the total spacetime is easy to define and locate in the stationary case; on the other hand, Apparent Horizon depends on the embedding of the surface in spacetime and hence it is somewhat tricky to define. But for numerical simulations in General Relativity, locating the Apparent Horizon helps one to excise the black hole region and the singularity to have a stable computation. Moreover, for stationary solutions the two horizons match. Here we give a detailed pedagogical exposition of the subject and work out the non-trivial case of a slowly moving and spinning black hole.