Quasi-equilibrium tidal folds of white dwarfs around rotating black holes in shift-symmetric Einstein--scalar--Gauss--Bonnet gravity

Abstract

We examine how the geometry of rotating black holes in linear, shift-symmetric Einstein--scalar--Gauss--Bonnet (EsGB) gravity changes the limiting tidal equilibria of white dwarfs (WDs). The relativistic tidal field is obtained from numerical EsGB backgrounds in a parallel-transported frame and coupled to a compressible affine model. Comparisons with Kerr black holes matched in Arnowitt--Deser--Misner (ADM) mass and angular momentum show a positive shift in the orbital frequency at the tidal fold. At fixed spin the relative correction follows an approximately quadratic dependence on the EsGB coupling, consistent with the leading response of the metric to the scalar field. Over the sampled backgrounds, the relative correction reaches order $10^{-3}$. Black hole rotation also changes the relation between the tidal fold and the innermost stable circular orbit (ISCO): the sampled prograde folds remain outside the ISCO, while retrograde folds move inside it at higher spins. Orbital orientation therefore controls whether tidal equilibrium is lost before the orbital stability limit is reached. For the stellar and black hole masses considered here, the characteristic gravitational wave (GW) frequencies fall in the millihertz band relevant to planned space based interferometers. Future GW observations capable of resolving deviations from Kerr predictions could constrain the EsGB coupling.