Post-Newtonian dynamics and black hole thermodynamics in Einstein-scalar-Gauss-Bonnet gravity

TL;DR

This paper investigates the post-Newtonian dynamics of black hole binaries in Einstein-scalar-Gauss-Bonnet gravity, deriving solutions and effective descriptions that incorporate scalar field effects and black hole entropy during inspiral.

Contribution

It constructs static black hole solutions at fourth order in the Gauss-Bonnet coupling and develops a skeletonized model linking black hole entropy to binary dynamics, including scalar field effects.

Findings

Finite Gauss-Bonnet contributions to fields without regularization.

Two-body Lagrangian computed at first post-Newtonian order.

Padé-resummed sensitivities for specific theories.

Abstract

We study the post-Newtonian dynamics of black hole binaries in Einstein-scalar-Gauss-Bonnet gravity theories. To this aim we build static, spherically symmetric black hole solutions at fourth order in the Gauss-Bonnet coupling $\alpha$. We then "skeletonize" these solutions by reducing them to point particles with scalar field-dependent masses, showing that this procedure amounts to fixing the Wald entropy of the black holes during their slow inspiral. The cosmological value of the scalar field plays a crucial role in the dynamics of the binary. We compute the two-body Lagrangian at first post-Newtonian order and show that no regularization procedure is needed to obtain the Gauss-Bonnet contributions to the fields, which are finite. We illustrate the power of our approach by Pad\'e-resumming the so-called "sensitivities," which measure the coupling of the skeletonized body to the scalar field, for some specific theories of interest.