Gravitational radiation timescales for extreme mass ratio inspirals

The capture and inspiral of compact stellar objects into massive black holes is an important source of low- frequency gravitational waves ( with frequencies similar to 1 - 100 mHz), such as those that might be detected by the planned Laser Interferometer Space Antenna ( LISA). Simulations of stellar clusters designed to study this problem typically rely on simple treatments of the black hole encounter that neglect some important features of orbits around black holes, such as the minimum radii of stable, nonplunging orbits. Incorporating an accurate representation of the orbital dynamics near a black hole has been avoided due to the large computational overhead. This paper provides new, more accurate expressions for the energy and angular momentum lost by a compact object during a parabolic encounter with a nonspinning black hole, and the subsequent inspiral lifetime. These results improve on the Keplerian expressions that are now commonly used and will allow efficient computational simulations to be performed that account for the relativistic nature of the spacetime around the central black hole in the system.