The Close Limit of Colliding Black Holes: An Update

Abstract

The collision of binary black holes is one of the primary expected sources of gravitational waves to be detected by the broadband interferometric gravitational wave telescopes currently under construction, like the LIGO project in the US, the British/German GEO project, the TAMA project in Japan and the French/Italian VIRGO project. A collision of two binary black holes can be divided into three distinct regimes. Initially, the black holes spiral around each other in quasi-Newtonian orbits. The radius of the orbits decrease due to the emission of gravitational radiation. Let us call this period the “inspiral” phase. The gravitational waves produced during this phase are well described by the post-Newtonian approximation. Notice that such an approximation does not provide a good description of the whole spacetime, since it breaks down close to each hole (to first approximation, the holes are singular point particles), but as long as the holes are far apart, this is not expected to be relevant from the point of view of the waveforms observed at infinity.∗) The gravitational waves from this phase of the collision correspond to a quasi-regular sinusoid whose frequency and amplitude increases with time as the holes start getting closer to each other, known as the “chirp”. Good descriptions of this approximation applied to the binary black hole case and appropriate references can be found in Blanchet et al. 2) When the separation of the holes is around 10 to 12 times the mass of each individual holes, it is expected that the post-Newtonian approximation breaks down. It is not completely clear what is the extent of the breakdown, since the post-Newtonian approximation leads to an asymptotic perturbation series. In fact, attempts are currently being made to extend the validity of the domain of the approximation using Pade approximants. 3) In any event, there will be a limiting separation of the holes such that if they are any closer, one cannot use the post-Newtonian approximation. The domain that starts at that point and continues up to the point in which the