Stuffed Black Holes

TL;DR

This paper introduces a method for constructing initial data for black hole spacetimes that are regular everywhere and suitable for numerical simulations, by matching interior and exterior metrics across the apparent horizon.

Contribution

It presents a novel approach to generate regular, complete initial data for black holes using conformal matching, applicable to multiple black hole configurations.

Findings

Constructed initial data for single and binary black holes.

Demonstrated regularity and completeness of the solutions.

Compared evolution of stuffed black holes with vacuum black holes.

Abstract

Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric is the vacuum solution obtained by the well known conformal imaging method. The interior metric for every black hole is regular everywhere and corresponds to a positive energy density. The resulting matched solutions cover then the whole initial (Cauchy) hypersurface, without any singularity, and can be useful for numerical applications. The simpler cases of one black hole (Schwarzschild data) or two identical black holes (Misner data) are explicitly solved. A procedure for extending this construction to the multiple black hole case is also given, and it is shown to work for all time symmetric vacuum solutions obtained by the conformal imaging method. The numerical evolution of one such 'stuffed' black hole is compared with that of a pure vacuum or 'plain' black hole in the spherically symmetric case.