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

Abstract

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. Our time-domain code reproduces the results of a recent frequency-domain calculation by Warburton and Barack, but has the added advantage of being readily adaptable to include the back-reaction from the self force in a self-consistent manner. In a forthcoming paper---the third in the series---we apply our method to the gravitational self-force (in the Lorenz gauge).

30 pages, 5 figures, 3 tables. To match published version

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• Static Kerr Green's Function in Closed Form and an Analytic Derivation of the Self-Force for a Static Scalar Charge in Kerr Space-Time
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• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
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• Tachyonic Instability of Reissner-Nordström-Melvin Black Holes in Einstein-Maxwell-Scalar Theory