On bare masses in time-symmetric initial-value solutions for two black holes

TL;DR

This paper rederives the Brill-Lindquist initial-value solution for two black holes using the Hamiltonian constraint, introducing bare masses and extending the approach to the Misner-Lindquist solution.

Contribution

It presents a new derivation of the initial-value solutions for binary black holes using the Hamiltonian constraint with delta sources, clarifying the concept of bare masses.

Findings

Rederived the Brill-Lindquist solution with Hamiltonian constraint.

Introduced the concept of bare masses for black holes.

Extended the method to the Misner-Lindquist solution.

Abstract

The Brill-Lindquist time-symmetric initial-value solution for two uncharged black holes is rederived using the Hamiltonian constraint equation with Dirac delta distributions as a source for the binary black-hole field. The bare masses of the Brill-Lindquist black holes are introduced in a way which is applied, after straightforward modification, to the Misner-Linquist binary black-hole solution.