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

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.

LaTeX, 4 pages

References in corpus (1)

• The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Cited by in corpus (7)

• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• A skeleton approximate solution of the Einstein field equations for multiple black-hole systems
• Binary black hole evolutions of approximate puncture initial data
• Lapse function for maximally sliced Brill-Lindquist initial data
• Tensor polarization of $\omega$ produced at threshold in $p-p$ collisions