Binary Black Holes Coalescence: Transition from Adiabatic Inspiral to Plunge

It seems likely that the first detection of gravitational waves with the LIGO/VIRGO/... interferometers will come from binary systems made of massive black holes of comparable masses, say with a total mass M ≃ 15M⊙ + 15M⊙. For such massive systems the gravitational-wave frequency at the last stable (circular) orbit (LSO) is very close to the location of the minimum of the detector’s noise spectral density. Therefore, for data analysis purposes it is quite desirable to have a thorough knowledge of the late dynamical evolution of comparable-mass binaries. When the two black holes become closer than ∼ 10M , the post-Newtonian (PN) expansion, which adequately describes the motion at large separations, cannot be trusted any more, and non-perturbative techniques should be used to deal with the non linearities and the strong curvature effects of the final phase of evolution. Despite the progress made by the numerical relativity community during the last years, an estimate of the complete waveform emitted by a comparable-mass black hole binary has not been provided, yet. Hence, to tackle this issue we have recently introduced a new non-perturbative analytical approach to the general relativistic two-body problem 1, 2 which should be able to capture the crucial features of the transition from the adiabatic phase to the plunge. Our approach combines two PN re-summation techniques. The first method 1 allows one to derive a non-perturbative estimate of the conservative part of the nonlinear force law determining the motion of comparable-mass binaries. The basic idea 1 is to map the conservative real two-body dynamics (up to 2PN order) onto an effective one-body one, where a test particle of mass μ ≡ m1 m2/M moves in some effective background metric g μν . As long as radiation reaction effects are not taken into account, the effective metric is just a deformation of the Schwarzschild metric with deformation parameter ν = μ/M . The effective description provides a way of re-summing in a non-perturbative manner the badly convergent PN-expanded