Close limit approximation for modified gravity: Scalar instabilities in binary black hole spacetimes

Abstract

The close limit approximation of binary black hole is a powerful method to study gravitational-wave emission from highly non-linear geometries. In this work, we use it as a tool to model black hole spacetimes in theories of gravity with a new fundamental scalar degree of freedom. As an example, we consider Einstein-scalar-Gauss-Bonnet gravity, which admits as solution the Schwarzschild geometry as well as black holes with scalar hair. Accordingly, we find scalar perturbations growing unbounded around binary systems. This "dynamical scalarization" process is easier to trigger (i.e. occurs at lower values of the coupling constant of the theory) than the corresponding process for isolated black holes. Our results and framework highlight the fundamental role of the interaction during the collision of compact objects. They also emphasize the importance of having waveforms for black hole binaries in alternative theories, in order to consistently perform tests beyond General Relativity.