Abstract

Gravitational wave observations allow us to probe directly the nature of black holes. This provides us with an unprecedented opportunity to test the gravitational sector. I will argue that effective field theory (EFT) techniques provide a natural framework to constrain possible departures from General Relativity (GR) in a model independent way.

To illustrate this point, in this talk I will focus on a particularly striking departure from the black hole solutions of GR, namely the existence of scalar hair (i.e. one or more scalar fields with a non-trivial radial profile). I will introduce an EFT for perturbations around spherically symmetric spacetimes with a scalar hair, and then discuss a couple of applications in different regimes.

First, I will apply this formalism to study quasi-normal modes (QNM) of static black holes with a scalar hair. Assuming that the deviation of the background from Schwarzschild is small, I will use a WKB approximation to introduce the notion of “light ring expansion”—an approximation analogous to the slow-roll expansion used for inflation—and provide a model independent parametrization of the QNM spectrum. Second, if time allows it, I will use this EFT to calculate the power emitted by an extreme mass-ratio binary inspiral in the post-Newtonian limit.