Dynamical hair growth in black hole binaries in Einstein-scalar-Gauss-Bonnet gravity

Within the framework of scalar-tensor theories of gravity, certain models can evade classical black hole no-hair theorems. A well-known example is Einstein-scalar-Gauss-Bonnet gravity, where black holes carrying a scalar charge can exist. We find that, within this theory, binary black holes initially described by General Relativity can acquire scalar charges once they reach a critical orbital separation ("dynamical scalarization"). We develop a simple semi-analytic model, based on the adiabatic conservation of the total Wald entropy, to estimate the scalar charge evolution during the binary inspiral. We also run fully nonlinear numerical-relativity simulations for different configurations, finding consistent results. The gravitational-wave phase difference between Einstein-scalar-Gauss-Bonnet and General Relativity waveforms, which we use to assess detectability, is also computed. We find that dynamical scalarization might be observable in nearly equal-mass binary black hole mergers with third-generation ground-based gravitational-wave detectors, in a narrow range of the dimensional coupling of the theory.