Complete initial value spacetimes containing black holes in general relativity: Application to black hole-disk systems

TL;DR

This paper introduces a new method for constructing complete initial data for spacetimes with black holes, capable of handling complex, nonaxisymmetric systems like black hole-disk configurations with high spin.

Contribution

The authors develop a minimal-assumption initial data formulation for Einstein's equations, enabling the modeling of realistic black hole systems including nonaxisymmetric, self-gravitating matter.

Findings

Successfully modeled a nonaxisymmetric black hole-disk system with high black hole spin.

Produced initial data for Kerr-Schild black holes and rotating neutron stars.

Demonstrated the method's ability to handle complex, realistic astrophysical scenarios.

Abstract

We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full metric) that contain a black hole. Contrary to most current studies the formulation requires minimal assumptions. For example, rather than imposing the form of the spatial conformal metric we impose 3 gauge conditions adapted to the coordinates describing the system under consideration. For stationary, axisymmetric spacetimes our method yields Kerr-Schild black holes in vacuum and rotating equilibrium neutron stars. We demonstrate the power of our new method by solving for the first time the whole system of Einstein equations for a nonaxisymmetric, self-gravitating torus in the presence of a black hole. The black hole has dimensionless spin $J_{\rm bh}/M_{\rm bh}^2=0.9918$, a rotation axis tilted at a $30^\circ$ angle with respect to the angular momentum of the disk, and a mass of $\sim 1/5$ of the disk.