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arXiv · 1801.09616

Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background

Donato Bini·Thibault Damour·Andrea Geralico·Chris Kavanagh
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Abstract

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the $z$-axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-order self-force contribution to Detweiler's redshift invariant up to the 8.5 post-Newtonian order. We check that our result is the same in both gauges, as appropriate for a gauge-invariant quantity, and agrees with the currently known 3.5 post-Newtonian results.

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Donato Bini, Thibault Damour, Andrea Geralico, Chris Kavanagh. 2018-01-29. Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background. https://doi.org/10.1103/physrevd.97.104022

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