Black Holes through the lenses of Effective Field Theory

The detection of gravitational waves emitted by black hole binaries opens a window to test the theory of General Relativity and to probe the dynamics of gravity in regimes otherwise inaccessible. To fully exploit this opportunity, it is necessary to understand which are the consistent and detectable deviations from General Relativity. To single out these possible deviations, one must also be able to recognize effects due to environmental perturbations of the binary system, as these may lead to departures within General Relativity from the waveform of an ideal isolated binary.In this thesis, we approach some aspects of both these theoretical challenges from the point of view of effective field theory.First, we study how to narrow down the space of theories that can describe detectable deviations from General Relativity based on consistency with the fundamental principles of our description of nature. We consider the simple example of General Relativity modified by the presence of a shift-symmetric scalar field coupled only to gravity. In this context, we first show that only a specific scalar-graviton interaction can lead to black holes different from what General Relativity predicts while being consistently included in an effective field theory description. Then we study how causality, unitarity and locality constrain this interaction. We show that if this interaction is strong enough to leave an imprint detectable with the next gravitational wave interferometers, then causality would require new degrees of freedom to appear at very low energies.In the second part of this work, we consider one example of environmental perturbation that can affect black hole mergers: a distant third body orbiting the black hole binary.To study efficiently such a system, we derive a worldline effective action describing the relativistic effects due to the third body on timescales much longer than the orbital periods. Using techniques from non-relativistic General Relativity, we obtain a description of the two orbits as two interacting particles endowed with multipole moments. We carry out these computations up to quadrupole order in the three-body interaction, including the leading relativistic corrections. This approach allows to study novel long timescale effects that can enhance the rate of orbital flips of the inner binary