Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse

TL;DR

This paper investigates the causal properties and dynamics of trapping horizons during spherical gravitational collapse, providing insights relevant for astrophysical black hole modeling and challenging the traditional event horizon concept.

Contribution

It offers a detailed analysis of trapping horizons' causal nature and dynamics in spherical collapse, incorporating pressure effects and numerical simulations, advancing practical understanding of black hole formation.

Findings

Trapping horizons can be spacelike, timelike, or null depending on collapse conditions.

The study connects horizon properties with the Misner-Sharp-Hernandez formalism.

Pressure influences the asymptotic behavior of ingoing trapping horizons.

Abstract

In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an "event horizon" which has some serious drawbacks for practical applications. We here present results from a study of the properties of both outgoing and ingoing trapping horizons, assuming strict spherical symmetry throughout. We have investigated their causal nature (i.e. whether they are spacelike, timelike or null), making contact with the Misner-Sharp- Hernandez formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity related to expansions of null geodesic congruences, and the other using the horizon velocity measured with respect to the collapsing matter. After an introduction to these concepts, we then implement them within numerical simulations of stellar collapse, revisiting pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen. Our presentation here is aimed firmly at "real world" applications of interest to astrophysicists and includes the effects of pressure, which may be important for the asymptotic behaviour of the ingoing horizon.