arXiv:2403.08864v1 Announce Type: new
Abstract: This is a third installment in a program to develop a method for alleviating the scale disparity in binary black hole simulations with mass ratios in the intermediate astrophysical range, where simulation cost is prohibitive while purely perturbative methods may not be adequate. The method is based on excising a “worldtube” around the smaller object, much larger than the object itself, replacing it with an analytical model that approximates a tidally deformed black hole. Previously (arXiv:2304.05329) we have tested the idea in a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in 3+1 dimensions on the SpECTRE platform. Here we take the significant further step of allowing the orbit to evolve radiatively, in a self-consistent manner, under the effect of back-reaction from the scalar field. We compute the inspiral orbit and the emitted scalar-field waveform, showing a good agreement with perturbative calculations in the adiabatic approximation. We also demonstrate how our simulations accurately resolve post-adiabatic effects (for which we do not have perturbative results). In this work we focus on quasi-circular inspirals. Our implementation will shortly be publicly accessible in the SpECTRE numerical relativity code.
Future Roadmap: Challenges and Opportunities
Challenges:
- Scale Disparity: One of the main challenges is the scale disparity in binary black hole simulations with mass ratios in the intermediate astrophysical range. The simulation cost is currently prohibitive, and purely perturbative methods may not be adequate. Overcoming this challenge will require developing a new method to alleviate the scale disparity.
- Computational Cost: The current method of excising a “worldtube” around the smaller object and replacing it with an analytical model still has limitations. The computational cost of this method needs to be optimized to make it more efficient and practical for larger-scale simulations.
- Accuracy: While the method shows good agreement with perturbative calculations in the adiabatic approximation, it is important to further improve accuracy by resolving post-adiabatic effects. This requires developing new techniques and algorithms to accurately capture the dynamics of the system.
Opportunities:
- Public Accessibility: The implementation of the method used in this study will be made publicly accessible in the SpECTRE numerical relativity code. This opens up opportunities for other researchers and scientists to use and build upon this work, potentially leading to further advancements in black hole simulations.
- Realistic Orbit Evolution: The significant further step of allowing the orbit to evolve radiatively under the effect of back-reaction from the scalar field introduces a more realistic aspect to the simulations. This opens up opportunities to study more complex scenarios and investigate the impact of dynamic interactions on black hole simulations.
In conclusion, the development of a method to alleviate the scale disparity in binary black hole simulations is an ongoing challenge. However, the current study has made significant progress by allowing the orbit to evolve radiatively and showing good agreement with perturbative calculations. The future roadmap involves addressing challenges related to scale disparity, computational cost, and accuracy, while also exploring opportunities for public accessibility and studying more realistic orbit evolution. The implementation of the method in the SpECTRE numerical relativity code is a positive step towards enabling further research and advancements in this field.