Exploring the no-hair theorem with LISA

TL;DR

This paper investigates how LISA can test the no-hair theorem by detecting deviations from general relativity in black hole ringdowns, using two complementary analysis methods to improve the accuracy of such tests.

Contribution

It introduces two approaches for testing deviations from GR in black hole ringdowns with LISA, demonstrating their effectiveness and the benefit of combining both methods for more precise results.

Findings

High accuracy recovery of injected deviation values.

Uncertainty of 5-10% on mode frequency deviations.

Forecasted parameter estimation precision across LISA's observable range.

Abstract

In this study, we explore the possibility of testing the no-hair theorem with gravitational waves from massive black hole binaries in the frequency band of the Laser Interferometer Space Antenna (LISA). Based on its sensitivity, we consider LISA's ability to detect possible deviations from general relativity (GR) in the ringdown. Two approaches are considered: an agnostic quasi-normal mode (QNM) analysis, and a method explicitly targeting the deviations from GR for given QNMs. Both approaches allow us to find fractional deviations from general relativity as estimated parameters or by comparing the mass and spin estimated from different QNMs. However, depending on whether we rely on the prior knowledge of the source parameters from a pre-merger or inspiral-merger-ringdown (IMR) analysis, the estimated deviations may vary. Under some assumptions, the second approach targeting fractional deviations from GR allows us to recover the injected values with high accuracy and precision. We obtain $(5\%, 10\%)$ uncertainty on ($\delta \omega, \delta \tau)$ for the $(3,3,0)$ mode, and $(3\%, 17\%)$ for the $(4,4,0)$ mode. As each approach constrains different features, we conclude that combining both methods would be necessary to perform a better test. In this analysis, we also forecast the precision of the estimated deviation parameters for sources throughout the mass and distance ranges observable by LISA.