Compact binary inspirals inside a galactic dark matter halo

Abstract

We model a celestial binary composed of a compact object and a central galactic (nonrotating) black hole as a reduced 2-body problem in a modified isotropic Schwarzschild spacetime parametrized by galactic compactness, C, which will serve also as the descriptor for the amount of the galactic dark matter halo. As the compact object orbits around the central galactic black hole, the system loses binding energy and angular momentum due to the release of gravitational waves. This paper includes a novel derivation of an isotropic spacetime metric for a galactic environment around a black hole, an analysis on the trajectory by radiation reaction of the compact object around the black hole, and finally, a sample gravitational waveform using the leading quadrupole approximation from a post-Newtonian treatment, given that the binary is in its early inspiral phase.