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

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 α. 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 Padé-resumming the so-called "sensitivities," which measure the coupling of the skeletonized body to the scalar field, for some specific theories of interest. arXiv:1909.05258v1 [gr-qc]

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“…If the body is a BH, its dimensionless scalar charge is proportional to the dimensionless coupling constant of the theory β ≡ q −2 ζ = α/m 2 p [23,47,48]. The explicit form of d(β) has been derived in [48]. Taking into account the different normalization conventions, one finds that, for instance, d = 2β + 73 30 β 2 + 15577 2520 β 3 + O(β 4 ) for Einsteindilaton Gauss-Bonnet gravity [23,47] (f (ϕ) = e ϕ ), while d = 2β + 73 60 β 3 for shift-symmetric sGB gravity [17,26] (f (ϕ) = ϕ).…”