The gravitational self-force is the finite, regular part of a field that diverges at the location of the small body. Extracting it cleanly is a non-trivial mathematical problem: at first order, mode-sum regularization based on locally subtracting Detweiler–Whiting singular fields is well established. At second order, the situation is substantially more subtle — the source itself diverges, and naive subtraction is no longer sufficient.
Our work establishes the mathematical foundations and delivers practical implementations across the regularization toolkit: mode-sum subtraction, effective-source decomposition, and puncture methods. We have developed second-order puncture schemes adapted for use with frequency-domain solvers, and we maintain close connections to the regularization literature in related fields such as classical electrodynamics and post-Newtonian theory.
Current focus:
- Second-order puncture schemes for Kerr backgrounds
- Gauge-invariant regularization strategies
- High-order mode-sum coefficients
- Cross-validation of regularization approaches across solver implementations