Energy and angular momentum flow into a black hole in a binary

As a black hole in a binary spirals in gradually from large separation, energy and angular momentum flow not only to infinity but also into or out of the hole. In addition, the hole’s horizon area increases slowly during this process. In this paper, the changes in the black hole’s mass, spin, and horizon area during inspiral are calculated for a hole in a circular binary with a companion body of possibly comparable mass. When the binary is composed of equal mass black holes that have spins aligned with the orbital angular momentum and are rapidly rotating (with spins 99.8% of their maximal values), it is found that the fractional increase in the surface area of each hole’s horizon is 1% by the time the binary spirals down to a separation b of $6M$ (where M is the binary’s total mass), and 7% down to $b=2M.\mathrm{}$ The flow of energy and angular momentum into the black holes’ horizons changes the number of gravitational-wave cycles in the LIGO band by no more than a tenth of a cycle by the time the binary reaches $b=2M.\mathrm{}$ The results obtained in this paper are relevant for the detection and analysis of gravitational waves from binary systems containing a black hole.