Self-force on a scalar charge in Kerr spacetime: Circular equatorial orbits

Niels Warburton and Leor Barack
Phys. Rev. D 81, 084039 – Published 20 April 2010

Abstract

We present a calculation of the scalar-field self-force (SSF) acting on a scalar-charge particle in a strong-field orbit around a Kerr black hole. Our calculation specializes to circular and equatorial geodesic orbits. The analysis is an implementation of the standard mode-sum regularization scheme: We first calculate the multipole modes of the scalar-field 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 angular-momentum 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 (Boyer-Lindquist) orbital radius r0. However, for prograde orbits we find that the radial SSF becomes attractive (inward pointing) for r0>rc(a), where rc is a critical a-dependent radius at which the radial SSF vanishes. The dominant conservative effect of the SSF in Schwarzschild spacetime is known to be of third post-Newtonian (3PN) order (with a logarithmic running). Our numerical results suggest that the leading-order PN correction due to the black hole’s spin arises from spin-orbit coupling at 3PN order, which dominates the overall SSF effect at large r0. In PN language, the change of sign of the radial SSF is attributed to an interplay between the spin-orbit term (ar04.5) and the Schwarzschild term (r05logr0).

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 9 March 2010

DOI:https://doi.org/10.1103/PhysRevD.81.084039

©2010 American Physical Society

Authors & Affiliations

Niels Warburton and Leor Barack

  • School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom

See Also

Self-force on a scalar charge in Kerr spacetime: Eccentric equatorial orbits

Niels Warburton and Leor Barack
Phys. Rev. D 83, 124038 (2011)

Self-force on a scalar charge in Kerr spacetime: Inclined circular orbits

Niels Warburton
Phys. Rev. D 91, 024045 (2015)

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 81, Iss. 8 — 15 April 2010

Reuse & Permissions
Access Options
Editorial
General Relativity Still Making Waves
September 24, 2015

Clifford Will discusses the importance of Einstein’s general theory of relativity and its relevance for physics research today.

General Relativity
2015 - General Relativity’s Centennial

The editors of the Physical Review journals have curated a collection of landmark papers on General Relativity to celebrate its centennial. These papers are currently free to read.

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×