Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime

Understand

This is the second in a series of papers aimed at developing a practical time-domain method for self-force calculations in Kerr spacetime.

• The key elements of the method are (i) removal of a singular part of the perturbation field with a suitable analytic "puncture" based on the Detweiler--Whiting decomposition, (ii) decomposition of the perturbation equations in azimuthal ($m$-)modes, taking advantage of the axial symmetry of the Kerr background, (iii) numerical evolution of the individual $m$-modes in 2+1-dimensions with a finite difference scheme, and (iv) reconstruction of the physical self-force from the mode sum.
• Here we report an implementation of the method to compute the scalar-field self-force along circular equatorial geodesic orbits around a Kerr black hole.
• This constitutes a first time-domain computation of the self force in Kerr geometry.