Two-body problem in modified gravities and EOB theory

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In general relativity, the effective-one-body (EOB) approach, which consists in reducing the two-body dynamics to the motion of a test particle in an effective static, spherically symmetric metric, has proven to be a very powerful framework to describe analytically the coalescence of compact binary systems.

In this seminar, we address its extension to modified gravities, considering first the example of massless scalar-tensor theories (ST). We reduce the ST two-body dynamics, which is known at second post-Keplerian order, to a simple parametrized deformation of the general relativistic EOB Hamiltonian, and estimate the ST corrections to the strong-field regime; in particular, the ISCO location and orbital frequency.

We then discuss the class of Einstein-Maxwell-dilaton (EMD) theories, which provide simple examples of "hairy" black holes. We compute the EMD post-Keplerian two-body Lagrangian, and show that it can, as well, be incorporated within the EOB framework. Finally, we highlight that, depending on their scalar environment, EMD black holes can transition to a regime where they strongly couple to the scalar and vector fields, inducing large deviations from the general relativistic two-body dynamics.