Approximate Black Holes for Numerical Relativity

TL;DR

This paper introduces approximate black hole solutions in Brans-Dicke theory, useful for numerical relativity, by deriving solutions close to Schwarzschild space-time that can aid in horizon boundary condition modeling.

Contribution

The paper presents a new class of approximate black hole solutions in Brans-Dicke theory, facilitating numerical relativity simulations with improved horizon boundary handling.

Findings

Solutions are close to Schwarzschild space-time.

Derived from a cubic transition equation with a small parameter.

Proposed as candidates for approximate black holes in simulations.

Abstract

Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $\omega=0$, are derived in the Schwarzschild line-element. The solutions are obtained from a cubic transition equation with one small parameter. The exterior space-time of one family of solutions is arbitrarily close to the exterior Schwarzschild space-time. These nontopological solitons have some similarity with soliton stars, and are proposed as candidates for {\em approximate black holes} for the use in numerical relativity, in particular for treatment of horizon boundary conditions.