Harmonic-gauge dipole metric perturbations for weak-field circular orbits in Schwarzschild spacetime

Abstract

We calculate the harmonic-gauge even l=1 mode of the linear metric perturbation (MP) produced by a particle in a weak-field circular orbit around a Schwarzschild black hole (BH). We focus on the Newtonian limit, i.e. the limit in which the mass M of the central BH approaches zero (while fixing the orbital radius and the small-object mass), and obtain explicit expressions for the MP in this limit. We find that the MP are anomalous in this limit, namely, they do not approach their standard, Coulomb-like, flat-space values. Instead, the MP grows on approaching the BH, and this growth becomes worse as M decreases. This anomalous behavior leads to some pathologies which we briefly discuss. We also derive here the next-order correction (in the orbital frequency $\Omega$) to the MP.

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References in corpus (4)

• Gravitational self force and gauge transformations
• Low multipole contributions to the gravitational self-force
• Scalar, electromagnetic, and gravitational self-forces in weakly curved spacetimes
• Gravitational self force by mode sum regularization

Cited by in corpus (4)

• Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Harmonic gauge perturbations of the Schwarzschild metric