Trapping Horizons as inner boundary conditions for black hole spacetimes

TL;DR

This paper introduces new inner boundary conditions for simulating dynamical black hole spacetimes, inspired by trapping horizon theory, improving numerical stability and consistency with stationary limits.

Contribution

It proposes a novel set of boundary conditions based on the dynamical trapping horizon framework for 3+1 constrained evolution schemes with excision.

Findings

Boundary conditions reduce to isolated horizon conditions in stationary limit

Enhance numerical construction of dynamical black hole spacetimes

Provide a characteristic analysis for radiative mode boundary conditions

Abstract

We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.