arXiv:2503.09678v1 Announce Type: new
Abstract: Using gravitational waves to probe the geometry of the ringing remnant black hole formed in a binary black hole coalescence is a well-established way to test Einstein’s theory of general relativity. However, doing so requires knowledge of when the predictions of black hole perturbation theory, i.e., quasi-normal modes (QNMs), are a valid description of the emitted gravitational wave as well as what the amplitudes of these excitations are. In this work, we develop an algorithm to systematically extract QNMs from the ringdown of black hole merger simulations. Our algorithm improves upon previous ones in three ways: it fits over the two-sphere, enabling a complete model of the strain; it performs a reverse-search in time for QNMs using a more robust nonlinear least squares routine called texttt{VarPro}; and it checks the variance of QNM amplitudes, which we refer to as “stability”, over an interval matching the natural time scale of each QNM. Using this algorithm, we not only demonstrate the stability of a multitude of QNMs and their overtones across the parameter space of quasi-circular, non-precessing binary black holes, but we also identify new quadratic QNMs that may be detectable in the near future using ground-based interferometers. Furthermore, we provide evidence which suggests that the source of remnant black hole perturbations is roughly independent of the overtone index in a given angular harmonic across binary parameter space, at least for overtones with $nleq2$. This finding may hint at the spatiotemporal structure of ringdown perturbations in black hole coalescences, as well as the regime of validity of perturbation theory in the ringdown of these events. Our algorithm is made publicly available at the following GitHub repository: https://github.com/keefemitman/qnmfinder.
Using gravitational waves to test general relativity
The study examines the use of gravitational waves to investigate the properties of black holes formed in binary black hole coalescences. By analyzing the ringdown phase of these events, the researchers aim to test Einstein’s theory of general relativity. However, to do so accurately, they need to understand the characteristics of the emitted gravitational waves, including their quasi-normal modes (QNMs) and their amplitudes.
An improved algorithm for extracting QNMs
In this work, the researchers present an algorithm that allows for the systematic extraction of QNMs from simulations of black hole mergers. Their algorithm offers three key improvements over previous methods:
- It fits over the two-sphere, enabling a more comprehensive model of the gravitational wave strain.
- It performs a reverse-search in time for QNMs using a more robust nonlinear least squares routine called VarPro.
- It checks the stability of QNM amplitudes over an interval matching the natural time scale of each QNM.
With these enhancements, the researchers demonstrate the stability of multiple QNMs and their overtones across the parameter space of quasi-circular, non-precessing binary black holes. They also discover new quadratic QNMs that may soon be detectable using ground-based interferometers.
Understanding the spatiotemporal structure of black hole perturbations
The study also provides evidence suggesting that the source of perturbations in the remnant black hole is largely independent of the overtone index for a given angular harmonic across the binary parameter space, at least for overtones with n <= 2. This finding offers insights into the spatiotemporal structure of perturbations in black hole coalescences and the validity of perturbation theory in the ringdown phase of these events.
Future opportunities and challenges
This work opens up several opportunities for future research and discoveries. The algorithm developed in this study can be applied to analyze more diverse binary black hole configurations and to investigate the stability of QNMs in those scenarios. Detecting and characterizing new QNMs can provide further evidence for the accuracy of Einstein’s theory and enhance our understanding of the fundamental properties of black holes.
There are, however, challenges that need to be addressed. As the sensitivity of ground-based interferometers increases, the detection and analysis of QNMs become more complex. Additionally, the algorithm may need further refinement to handle different types of perturbations and to improve accuracy in extreme parameter regimes. Nonetheless, the availability of the algorithm on a public GitHub repository allows for collaboration and further development by the scientific community.
Conclusion
This study presents an improved algorithm for extracting quasi-normal modes from the ringdown phase of binary black hole mergers. The algorithm enables the identification of stable QNMs and the discovery of new ones. The findings also provide insights into the spatiotemporal structure of black hole perturbations and the validity of perturbation theory. Future research should focus on applying the algorithm to more diverse scenarios and addressing challenges related to detection and analysis. Overall, this work contributes to our understanding of general relativity and the properties of black holes.
GitHub Repository: https://github.com/keefemitman/qnmfinder