The gravitational recoil or “ kick ” of a black hole formed from the merger of two orbiting black holes , and caused by the anisotropic emission of gravitational radiation , is an astrophysically important phenomenon .
We combine ( i ) an earlier calculation , using post-Newtonian theory , of the kick velocity accumulated up to the merger of two non-spinning black holes , ( ii ) a “ close-limit approximation ” calculation of the radiation emitted during the ringdown phase , and based on a solution of the Regge-Wheeler and Zerilli equations using initial data accurate to second post-Newtonian order .
We prove that ringdown radiation produces a significant “ anti-kick ” .
Adding the contributions due to inspiral , merger and ringdown phases , our results for the net kick velocity agree with those from numerical relativity to 10–15 percent over a wide range of mass ratios , with a maximum velocity of 180 km/s at a mass ratio of 0.38 .