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

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 tool model spacetimes in theories gravity with new fundamental scalar degree freedom. As an example, consider Einstein-scalar-Gauss-Bonnet gravity, which admits solution the Schwarzschild geometry well holes hair. Accordingly, find perturbations growing unbounded around systems. This "dynamical scalarization" process easier trigger (i.e. occurs at lower values coupling constant theory) than corresponding for isolated holes. Our results and framework highlight role interaction during collision compact objects. They also emphasize importance having waveforms binaries alternative theories, order consistently perform tests beyond General Relativity.