A simple construction of initial data for multiple black holes

TL;DR

This paper presents a simplified method for constructing initial data for multiple black holes in vacuum, avoiding complex boundary conditions and ensuring solution existence and uniqueness.

Contribution

It introduces a new approach that compactifies internal regions, simplifying numerical implementation compared to traditional throat-based methods.

Findings

Simplified initial data construction for multiple black holes.

Proved existence and uniqueness of solutions to the Hamiltonian constraint.

Reduces computational complexity in numerical relativity simulations.

Abstract

We consider the initial data problem for several black holes in vacuum with arbitrary momenta and spins on a three space with punctures. We compactify the internal asymptotically flat regions to obtain a computational domain without inner boundaries. When treated numerically, this leads to a significant simplification over the conventional approach which is based on throats and isometry conditions. In this new setting it is possible to obtain existence and uniqueness of solutions to the Hamiltonian constraint.