Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet Gravity

TL;DR

This paper derives the effective two-body potential for spinning black hole binaries in Einstein-Scalar-Gauss-Bonnet gravity up to 3PN order using an EFT approach, incorporating scalar and spin effects for the first time.

Contribution

It extends the post-Newtonian formalism to include spin effects in ESGB gravity and derives the first effective potential at 3PN order for spinning black holes.

Findings

Derived the 3PN order two-body potential for spinning BHs in ESGB gravity.

Obtained BH sensitivities through a matching procedure with analytic solutions.

Analyzed thermodynamic properties of rotating BH solutions in ESGB.

Abstract

We explore the post-Newtonian dynamics of spinning black hole (BH) binaries in Einstein-ScalarGauss-Bonnet (ESGB) gravity, a theory that modifies general relativity by introducing a massless scalar field coupled nonminimally to gravity via the Gauss-Bonnet term. By employing an effective field theory (EFT) approach, we extend the Routhian formalism to incorporate spin effects in scalar interactions. In this formalism, we derive for the first time the effective two-body potential for spinning BHs up to the third post-Newtonian (3PN) order in generic ESGB gravity theories. This potential is expressed in terms of the sensitivities of the BHs, which are then obtained through a matching procedure using analytic BH solutions derived here within a slow-rotation approximation, accurate to seventh order in the Gauss-Bonnet coupling and fifth order in the BH spin. We also examine the thermodynamic properties of these rotating solutions, which, as shown in previous work, yield important insights into the inspiral phase evolution in ESGB gravity.