Quasi-normal modes of slowly-rotating Johannsen black holes

TL;DR

This paper investigates the quasi-normal modes of slowly-rotating Johannsen black holes to test deviations from General Relativity using gravitational wave data, deriving formulas and constraining deformation parameters.

Contribution

It provides a new fitting formula for quasi-normal modes of Johannsen black holes under slow rotation and constrains deformation parameters using GW170104 data.

Findings

Deformation parameter α13 significantly affects quasi-normal modes.

Derived fitting formulas valid for slow rotation (a* < 0.4).

GW170104 data are consistent with General Relativity predictions.

Abstract

The detection of gravitational waves with ground-based laser interferometers has opened a new window to test and constrain General Relativity (GR) in the strong, dynamical, and non-linear regime. In this paper, we follow an agnostic approach and we study the quasi-normal modes of gravitational perturbations of Johannsen black holes under the assumptions of the validity of the Einstein Equations and of low values of the black hole spin parameter and deformation parameters. We find that the deformation parameter $\alpha_{13}$ has a stronger impact on the quasi-normal modes than the other leading order deformation parameters ($\alpha_{22}$, $\alpha_{52}$, and $\epsilon_{3}$). We derive a fitting formula for the fundamental modes with $l=2$ and $l=3$ for the deformation parameter $\alpha_{13}$ valid in the slow rotation approximation ($a_* < 0.4$). Finally, we constrain $\alpha_{13}$ from the event GW170104; within our analysis, we find that the data of GW170104 are consistent with the predictions of GR.