# Science with the TianQin observatory: Preliminary results on testing the no-hair theorem with ringdown signals

## TL;DR

This paper evaluates TianQin's potential to test the no-hair theorem using black hole ringdown signals, showing it can constrain deviations from general relativity with high precision, especially for lower mass black holes.

## Contribution

It provides the first detailed analysis of TianQin's capability to test the no-hair theorem through ringdown signals, including parameter estimation and comparison with LISA.

## Key findings

- TianQin can constrain deviations in ringdown frequencies and decay times to within 0.2% and 1.5%.
- TianQin and LISA are highly complementary in black hole mass ranges.
- TianQin is most effective for lower mass black holes in testing the no-hair theorem.

## Abstract

We study the capability of the space-based gravitational wave observatory TianQin to test the no-hair theorem of General Relativity, using the ringdown signal from the coalescence of massive black hole binaries. We parameterize the ringdown signal by the four strongest quasinormal modes and estimate the signal to noise ratio for various source parameters. We consider constraints both from single detections and from all the events combined throughout the lifetime of the observatory, for different astrophysical models. We find that at the end of the mission, TianQin will have constrained deviations of the frequency and decay time of the dominant 22 mode from the general relativistic predictions to within 0.2% and 1.5% respectively, the frequencies of the subleading modes can be also constrained within 0.3%. We also find that TianQin and LISA are highly complementary, by virtue of their different frequency windows. Indeed, LISA can best perform ringdown tests for black hole masses in excess of $\sim 3\times 10^6 M_\odot$, while TianQin is best suited for lower masses.