Gravitational-Wave Energy Flux for Compact Binaries through Second Order in the Mass Ratio

Abstract

Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field and they agree remarkably well with numericalrelativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modelling extreme-mass-ratio inspirals and will be useful in modelling intermediate-mass-ratio systems.

Asymptotically matched quasi-circular inspiral and transition-to-plunge in the small mass ratio expansion

“…∂V geo ∂r = Γ r rr (e 2 − V geo ) + U 2 Γ r µν ξ µ ξ ν . (13) Comparing the writings of the radial self-force in Eqs. (9) and (11) and using the identities e − 1…”

“…One of the main motivation for developing methods in the small mass ratio limit is the prospect of observations of EMRIs (extreme mass ratio inspirals) by LISA [11]. Another motivation is the recent realization that, even when restricting to the first post-adiabatic approximation, the small mass ratio expansion is applicable to intermediate mass binaries and, up to a certain extent, to equal mass binaries [12,13].…”

Numerical-relativity validation of effective-one-body waveforms in the intermediate-mass-ratio regime

“…The evolution of these large mass ratio binaries has been approached via perturbation theory and the computation of the gravitational self-force exerted by the field of the small black hole on itself [5][6][7][8][9][10][11]. The resolution of the binary black hole problem in its full nonlinearity has been only possible after the 2005 breakthroughs in numerical relativity (NR) [12][13][14], and a first proof of principle has been performed in [15] for the 100:1 mass ratio case, following studies of the 10:1 and 15:1 [16] ones.…”

Prospects for determining the nature of the secondaries of extreme mass-ratio inspirals using the spin-induced quadrupole deformation

“…Furthermore, an exciting extension of the work includes the contribution of the secondorder self-force based on the two-time scale method [74]. Several authors recently studied such effects for EMRI systems consisting of a massive Schwarzschild black hole and a point particle [104][105][106]. It is assertive to consider the effect of second-order self-force in the presence of spinning binaries, which we left for the future.…”