Distributional sources for black hole initial data

TL;DR

This paper introduces a novel approach to generating black hole initial data using distributional sources, extending traditional methods and providing new insights into spin and momentum parameters.

Contribution

It reformulates the puncture method with distributions as source terms, generalizing initial data for black holes beyond existing Bowen-York formulations.

Findings

Bowen-York data and trumpet variations are generated by distributional sources.

Distributional sources can encode spin and momentum of black holes.

New families of initial data with generalized sources are constructed.

Abstract

Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the system as parameters of the initial data. In an attempt to extend these benefits to other formulations of the Einstein constraints, the puncture method is reformulated using distributions as source terms. It is shown how the Bowen-York puncture black hole initial data and the trumpet variation is generated by distributional sources. A heuristic argument is presented to argue that these sources are the general sources of spin and momentum. In order to clarify the meaning of other distributional sources, an exact family of initial data with generalized sources to the Hamiltonian constraint are studied; spinning trumpet black hole initial data and black hole initial data with higher order momentum sources are also studied.