Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole

Abstract

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar ψ4 using semi-analytical methods. The metric perturbation is then reconstructed from ψ4 in an (outgoing) radiation gauge, adding the appropriate non-radiative contributions arising from the shifts in mass and angular momentum of the spacetime.As a demonstration we calculate the generalized redshift U as a function of the orbital frequencies Ωr and Ω φ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of U . In Kerr, we provide completely novel values of U for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper. * M.vandeMeent@soton.ac.uk † a.g.shah@soton.ac.uk 1. Homogeneous solutions (generic case ωmn = 0 and ma = 0)

New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant

“…For the present computation we closely follow the standard Teukolsky perturbation scheme as discussed in detail in Refs. [14,25] and already adopted in our previous work [21] (see also the Appendix A there), so we limit below to provide the necessary information on intermediate steps. Our computed quantity h uk t is regularized by subtracting its PN-analytically computed large-l limit (we refer, e.g., to Section IIIB of Ref.…”

Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime

“…The third approach III, instead, uses purely a scalar harmonic projection. [17] so that the GSF piece δψ(y) in ψ(y) (such that ψ(y) =…”

“…This paper is concerned with phenomena associated with extreme mass-ratio inspirals, a source for LISA which is most naturally described using GSF. Of particular interest has been the identification of gauge invariant physical effects of the conservative self-force, for example the well known periastron advance [10,11] and redshift invariants [12][13][14][15][16][17][18][19][20]; for a recent review of this topic see [21]. These invariants rely on the delicate regularization techniques for dealing with the singular nature of the point like source.…”

Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits

“…Progress is also being made on understanding and calculating the second-order GSF [30][31][32][33][34][35][36]. In the case of Kerr EMRIs, steady developments have been made in GSF calculations for circular and bound equatorial orbits [37][38][39][40][41][42][43]. Progress has now been reported [44] in calculating the GSF on generic Kerr orbits.…”