Gravitational Waves from Equatorial Eccentric EMRI Systems: Relativistic Corrections to the Quadrupole Formula

A stellar-mass compact object spiraling into a massive black hole on a slowly shrinking, eccentric and equatorial orbit will emit gravitational radiation detectable by LISA. Computing the orbital evolution and emitted gravitational waves from a system with arbitrary orbital parameters is possible via two techniques: the expensive numerical fully relativistic Teukolsky-Sasaki-Nakamura formalism, and the analytic quadrupole formula. Comparing predictions of the gravitational wave luminosity from the quadrupole formula to select cases computed via the TSN formalism will provide the groundwork for quick, accurate predictions of the evolution of arbitrary EMRI orbits. This work bridges the gap between the two methods by determining relativistic corrections to the quadrupole formula, extending the methods of Finn and Thorne (2000) to eccentric orbits.