Selfforce on a scalar charge in Kerr spacetime: Circular equatorial orbits
Abstract
We present a calculation of the scalarfield selfforce (SSF) acting on a scalarcharge particle in a strongfield orbit around a Kerr black hole. Our calculation specializes to circular and equatorial geodesic orbits. The analysis is an implementation of the standard modesum regularization scheme: We first calculate the multipole modes of the scalarfield perturbation using numerical integration in the frequency domain, and then apply a certain regularization procedure to each of the modes. The dissipative piece of the SSF is found to be consistent with the flux of energy and angularmomentum carried by the scalar waves through the event horizon and out to infinity. The conservative (radial) component of the SSF is calculated here for the first time. When the motion is retrograde this component is found to be repulsive (outward pointing, as in the Schwarzschild case) for any spin parameter a and (BoyerLindquist) orbital radius r_{0}. However, for prograde orbits we find that the radial SSF becomes attractive (inward pointing) for r_{0}>r_{c}(a), where r_{c} is a critical adependent radius at which the radial SSF vanishes. The dominant conservative effect of the SSF in Schwarzschild spacetime is known to be of third postNewtonian (3PN) order (with a logarithmic running). Our numerical results suggest that the leadingorder PN correction due to the black hole’s spin arises from spinorbit coupling at 3PN order, which dominates the overall SSF effect at large r_{0}. In PN language, the change of sign of the radial SSF is attributed to an interplay between the spinorbit term (∝ar_{0}^{4.5}) and the Schwarzschild term (∝r_{0}^{5}logr_{0}).
 Publication:

Physical Review D
 Pub Date:
 April 2010
 DOI:
 10.1103/PhysRevD.81.084039
 arXiv:
 arXiv:1003.1860
 Bibcode:
 2010PhRvD..81h4039W
 Keywords:

 04.25.Nx;
 04.25.g;
 04.70.Bw;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Approximation methods;
 equations of motion;
 Classical black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 22 pages, 10 eps figures, correct horizon boundary condition