Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation

TL;DR

This paper introduces a new numerical method for constructing quasiequilibrium models of black hole-neutron star binaries within general relativity, focusing on strong-field interactions and tidal disruption.

Contribution

It develops a novel approach combining the conformal thin-sandwich formalism with Kerr-Schild backgrounds to model black hole-neutron star systems in quasiequilibrium.

Findings

Validated the numerical method through code tests.

Compared relativistic models with Newtonian approximations.

Identified the conditions for tidal disruption in strong gravity.

Abstract

We present a new numerical method for the construction of quasiequilibrium models of black hole-neutron star binaries. We solve the constraint equations of general relativity, decomposed in the conformal thin-sandwich formalism, together with the Euler equation for the neutron star matter. We take the system to be stationary in a corotating frame and thereby assume the presence of a helical Killing vector. We solve these coupled equations in the background metric of a Kerr-Schild black hole, which accounts for the neutron star's black hole companion. In this paper we adopt a polytropic equation of state for the neutron star matter and assume large black hole--to--neutron star mass ratios. These simplifications allow us to focus on the construction of quasiequilibrium neutron star models in the presence of strong-field, black hole companions. We summarize the results of several code tests, compare with Newtonian models, and locate the onset of tidal disruption in a fully relativistic framework.