Gravitational self-torque and spin precession in compact binaries

Abstract

We calculate the effect of self-interaction on the "geodetic" spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle ψ per radian of orbital revolution for a particle carrying mass μ and spin s ≪ ðG=cÞμ 2 in a circular orbit around a Schwarzschild black hole of mass M ≫ μ. We compute ψ through Oðμ=MÞ in perturbation theory, i.e, including the correction δψ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for δψ, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semianalytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches.

Experimental mathematics meets gravitational self-force

“…(29) in [53] and our Eqs. (6) and (9) where we have noted that ∆U comes from the metric perturbation and are using the same notation as in Sec.…”

“…One then solves the resulting expression for α N,0 to obtain Eq. (29). One derives the more involved expressions for more complicated cases with more terms and more radii in the same way by solving a linear system, which Mathematica will do quite efficiently.…”

“…Apart from ∆U , high-order PN coefficients of other invariants from which the EOB formalism can benefit have also been calculated: These are the linear-in-mass ratio conservative corrections to the spin-precession angle [29] and the quadrupolar [30] and octupolar [31] tidal invariants (the eigenvalues of the electric-and magnetic-type tidal tensors), all which have been calculated to high PN order in [27,[31][32][33][34]. Recently, Bernuzzi et al [35] introduced a semi-analytical tidally coupled binary neutron star model using the EOB theory where information from the PN expansion of the redshift and tidal invariants was incorporated (using the tidal results from Bini and Damour [33]).…”

Sources of Gravitational Waves: Theory and Observations

“…Thus, the knowledge of the redshift can be employed to compute relativistic effects linear in q in the (specific) binding energy and angular momentum [148,262,263]. Other dynamical invariants have also been derived [264][265][266].…”

Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III. Spin-orbit coupling revisited

“…Spin effects on gravitating systems were considered in [11], the gravitational self-torque and spin precession in [12], precession dynamics in numerical relativity and post-Newtonian approximation in [13], and within the context of the effective one body approach in [14]. Selfforce effects on the gravitational waveforms contributing to Φ (1) within the post-Newtonian approach were considered in [15], and second-order self forces were studied in Refs.…”