  The capture and inspiral of compact stellar masses into massive black holes
is an important source of low-frequency gravitational waves (with frequencies
of ~1-100mHz), 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 which neglect some important features of orbits around black holes,
such as the minimum radii of stable, non-plunging 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 non-spinning black hole, and the
subsequent inspiral lifetime. These results improve on the Keplerian
expressions which 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.
