Black hole initial data without elliptic equations

TL;DR

This paper introduces a novel method for generating initial data for black holes in general relativity that avoids elliptic equations, demonstrating its effectiveness on perturbed Schwarzschild black holes and discussing potential extensions.

Contribution

The paper presents a new approach to solving Einstein's constraint equations without elliptic equations, applicable to black hole initial data, and proves its well-posedness for certain cases.

Findings

Successfully applied to a nonlinear perturbation of Schwarzschild black hole

Established well-posedness of the new constraint problem

Discussed potential for generalization to multiple, spinning black holes

Abstract

We explore whether a new method to solve the constraints of Einstein's equations, which does not involve elliptic equations, can be applied to provide initial data for black holes. We show that this method can be successfully applied to a nonlinear perturbation of a Schwarzschild black hole by establishing the well-posedness of the resulting constraint problem. We discuss its possible generalization to the boosted, spinning multiple black hole problem.