Speaker : J. Thornburg

Title : Scalar self-force for highly eccentric orbits in Kerr spacetime

Abstract : We consider the problem of computing the self-force for a scalar-field particle on a bound eccentric orbit (which need not be a geodesic) in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization followed by an ("-mode") Fourier decomposition and a separate time-domain numerical evolution in 2+1 dimensions for each . We introduce a finite worldtube which surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region the worldtube moves to follow the particle’s orbital motion. Our numerical evolution uses Berger-Oliger mesh refinement with 4th order finite differencing in space and time. We use slices of constant Boyer-Lindquist time near the black hole, deformed to be asymptotically hyperboloidal and compactified near the horizon and . Our computational scheme allows computation for highly eccentric orbits, and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations ("wiggles") in the self-force on the outgoing leg of the orbit shortly after periastron passage ; these appear to be caused by the passage of the particle close to the background Kerr black hole.