Probing Kerr symmetry breaking with LISA extreme-mass-ratio inspirals

Abstract

[abridged] Extreme-mass-ratio inspirals (EMRIs) are one of the main sources of gravitational waves (GWs) for LISA. The large number of GW cycles in the EMRI signal makes them very precise probes of the local spacetime geometry that are highly sensitive to deviations from the Kerr metric. Here, we investigate EMRIs around generic, non-Kerr compact objects characterized by a rich multipolar structure. At leading post-Newtonian and linear mass-ratio orders, we incorporate in the waveform model both the axisymmetric and nonaxisymmetric components of the mass quadrupole and octupole moments, parametrizing in this way the breaking of two fundamental symmetries of the Kerr metric. We study the impact of these modifications on the waveform in the philosophy of the EMRI \emph{analytic kludge} models. In our case, the orbital evolution follows from a Lagrangian that contains of the multipolar structure of the primary, including for the first time the nonaxisymmetric multipole moments that break axial symmetry. Then, we assess the capability of LISA to constrain deviations of the multipole moments from their Kerr values and detecting symmetry-breaking effects. In this way, we analyze how effectively LISA will be able to probe models that predict horizon-scale modifications, such as the fuzzball model. Our results show that future LISA observations of EMRIs will provide unprecedented tests of the black hole structure and the underlying theory of gravity. In particular, with one year of LISA data from the inspiral of a $10\,M_{\odot}$ compact object into a rotating supermassive black hole of $10^{6}\,M_{\odot}$ and signal-to-noise ratio of 30, it will be possible to place tight bounds on deviations from the two fundamental symmetries of the Kerr metric, constraining equatorial symmetry breaking in the mass multipole sector to the $10^{-1}$ level and axial symmetry breaking to the $10^{-2}$ level.