An introduction to local Black Hole horizons in the 3+1 approach to General Relativity

TL;DR

This paper introduces dynamical trapping horizons within the 3+1 approach to General Relativity, emphasizing their geometric properties and applications in numerical black hole simulations.

Contribution

It provides a comprehensive overview of quasi-local black hole horizons, highlighting their geometric features and dual role in Einstein equation formulations and spacetime analysis.

Findings

Analysis of the geometric and structural properties of dynamical trapping horizons.

Discussion of their role in numerical evolution and diagnosis of black hole spacetimes.

Emphasis on the rigidity and probing capabilities of these horizons in strong-field regimes.

Abstract

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an "a priori" ingredient in certain formulations of Einstein equations and as an "a posteriori" tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the "rigidity" properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.