arXiv:2505.07941v1 Announce Type: new
Abstract: We engage with the challenge of calculating the waveforms of gravitational waves emitted by spinless binary black hole merger in extreme mass-ratio limit. We model the stellar-mass black hole as a test-particle, initially on a circular orbit, that undergoes adiabatic inspiral until it reaches the innermost stable circular orbit (ISCO), after which it follows a geodesic trajectory. We compute the gravitational waveforms emitted during both phases — before and after the ISCO crossing — and demonstrate how to accurately connect them. While the waveforms are calculated adiabatically up to the ISCO, the associated phase error near the ISCO scales as $nu^{1/5}$ and remains below one radian for sufficiently small mass-ratios $nu$. Our complete waveform is universal in the sense that all computationally expensive calculations are performed once, and its application to any binary merger can be obtained by appropriately re-scaling time, phase, and amplitude. We compare our results with existing models in the literature and show that our complete waveforms are accurate enough all the way from separations that are an order of one gravitational radii outside the ISCO, to the merger.
Future Roadmap
Based on the conclusions of the text, readers can expect the following roadmap for future exploration in the field of calculating gravitational waveforms:
Potential Challenges:
- Ensuring accurate connection of waveforms before and after the ISCO crossing.
- Reducing phase error near the ISCO, particularly for larger mass-ratios.
Opportunities on the Horizon:
- Developing universal waveform models that are applicable to any binary merger with proper scaling.
- Exploring applications of complete waveform models in various astrophysical contexts.
Conclusion:
Advancements in calculating gravitational waveforms for black hole mergers hold promise for future discoveries in astrophysics and gravitational wave astronomy. By addressing current challenges and leveraging upcoming opportunities, researchers can further enhance our understanding of extreme mass-ratio events in the universe.