Overcoming the Gauge Problem for the Gravitational Self-Force

TL;DR

This paper introduces a new method for calculating the gravitational self-force in alternative gauges, improving efficiency and potentially enabling progress in modeling Kerr black hole systems for gravitational wave detection.

Contribution

A novel scheme based on the Particle-without-Particle formulation allows self-force computation from wave equations in gauges like Regge-Wheeler, facilitating future Kerr black hole analyses.

Findings

Enables self-force calculations in gauges other than Lorenz.

Simplifies the computational process by using wave-type equations.

Potentially applicable to Kerr black holes.

Abstract

The gravitational waves emitted by binary systems with extreme-mass ratios carry unique astrophysical information that can only be detected by space-based detectors like eLISA. To that end, a very accurate modelling of the system is required. The gravitational self-force program, which has been fully developed in the Lorenz gauge, is the best approach we have so far. However, the computations required would be done more efficiently if we could work in other gauges, like the Regge-Wheeler (RW) one in the case of Schwarzschild black holes. In this letter we present a new scheme, based on the Particle-without-Particle formulation of the field equations, where the gravitational self-force can be obtained from just solving individual wave-type equations like the master equations of the RW gauge. This approach can help to tackle the yet unsolved Kerr case.