Entropic force in black hole binaries and its Newtonian limits

TL;DR

This paper derives an exact static force between black holes using entropy principles, connects it to Newtonian gravity, and introduces new laws for entropy changes during mergers, providing a unified thermodynamic view of gravity.

Contribution

It presents a novel exact solution for black hole binary forces based on entropy and extends Newtonian gravity through a new variational principle involving apparent horizons.

Findings

Exact force solution for black hole binaries at turning points

New power laws for entropy jumps during mergers

Gravity derived from an adiabatic variational principle

Abstract

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.