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

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.

16 pages, 1 figure, revtex macros used

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• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Self-Force Calculations with a Spinning Secondary
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Dissipation in extreme-mass ratio binaries with a spinning secondary
• Analytic post-Newtonian expansion of the energy and angular momentum radiated to infinity by eccentric-orbit non-spinning extreme-mass-ratio inspirals to 19PN
• Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Gravitational self-force corrections to tidal invariants for spinning particles on circular orbits in a Schwarzschild spacetime
• Multipolar Particles in Helically Symmetric Spacetimes