Introduction to dynamical horizons in numerical relativity

TL;DR

This paper introduces a quasi-local method within the dynamical horizon framework to analyze evolving black holes in numerical simulations, including locating marginal surfaces, calculating mass, angular momentum, and fluxes, and verifying black hole settling to Kerr solutions.

Contribution

It extends the dynamical horizon framework to time-dependent scenarios, providing new tools for locating horizons, computing physical quantities, and analyzing black hole evolution in numerical relativity.

Findings

Successfully locates and studies the evolution of marginal surfaces.

Calculates black hole mass, angular momentum, and multipole moments in dynamical situations.

Analyzes energy fluxes and black hole growth during simulations.

Abstract

This paper presents a quasi-local method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent situations. In particular: (i) We locate various kinds of marginal surfaces and study their time evolution. An important ingredient is the calculation of the signature of the horizon, which can be either spacelike, timelike, or null. (ii) We generalize the calculation of the black hole mass and angular momentum, which were previously defined for axisymmetric isolated horizons to dynamical situations. (iii) We calculate the source multipole moments of the black hole which can be used to verify that the black hole settles down to a Kerr solution. (iv) We also study the fluxes of energy crossing the horizon, which describes how a black hole grows as it accretes matter and/or radiation. We describe our numerical implementation of these concepts and apply them to three specific test cases, namely, the axisymmetric head-on collision of two black holes, the axisymmetric collapse of a neutron star, and a non-axisymmetric black hole collision with non-zero initial orbital angular momentum.