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Octupolar invariants for compact binaries on quasi-circular orbits · Around

2015

Octupolar invariants for compact binaries on quasi-circular orbits

Nolan, Patrick, Kavanagh, Chris, Dolan, Sam R et al.

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We extend the gravitational self-force methodology to identify and compute new $O(\mu)$ tidal invariants for a compact body of mass $\mu$ on a quasi-circular orbit about a black hole of mass $M \gg \mu$.

In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative `electric' invariants and 3+1 `magnetic' invariants, satisfying 1+1 and 1+0 trace conditions.
After formulating for equatorial circular orbits on Kerr spacetime, we calculate explicitly for Schwarzschild spacetime.
We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi.

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