Thermodynamics of binary black holes and neutron stars

TL;DR

This paper explores the thermodynamics and stability of binary black hole and neutron star systems in general relativity, deriving laws relating mass, angular momentum, and horizon properties, with implications for equilibrium and stability analysis.

Contribution

It establishes an exact first law for binary systems with helical symmetry, linking changes in Noether charge to fluid and horizon properties, and analyzes stability criteria.

Findings

Derivation of an exact first law relating system parameters.

Identification of conditions for equilibrium and stability.

Application of the first law to approximate asymptotic regimes.

Abstract

We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k^\alpha, heuristically, the generator of time-translations in a corotating frame. Systems that are stationary in this sense are not asymptotically flat, but have asymptotic behavior corresponding to equal amounts of ingoing and outgoing radiation. For black-hole binaries, a rigidity theorem implies that the Killing vector lies along the horizon's generators, and from this one can deduce the zeroth law (constant surface gravity of the horizon). Remarkably, although the mass and angular momentum of such a system are not defined, there is an exact first law, relating the change in the asymptotic Noether charge to the changes in the vorticity, baryon mass, and entropy of the fluid, and in the area of black holes. Binary systems with M\Omega small have an approximate asymptopia in which one can write the first law in terms of the asymptotic mass and angular momentum. Asymptotic flatness is precise in two classes of solutions used to model binary systems: spacetimes satisfying the post-Newtonian equations, and solutions to a modified set of field equations that have a spatially conformally flat metric. (The spatial conformal flatness formalism with helical symmetry, however, is consistent with maximal slicing only if replaces the extrinsic curvature in the field equations by an artificially tracefree expression in terms of the shift vector.) For these spacetimes, nearby equilibria whose stars have the same vorticity obey the relation \delta M = \Omega \delta J, from which one can obtain a turning point criterion that governs the stability of orbits.