Second-order self-force calculation of the gravitational binding energy in compact binaries

TL;DR

This paper presents the first complete scheme for second-order self-force calculations in EMRIs, enabling more accurate modeling of gravitational binding energy for quasicircular orbits around Schwarzschild black holes, crucial for gravitational wave detection.

Contribution

It introduces a novel implementation of second-order self-force computations specifically for quasicircular orbits in Schwarzschild spacetime, advancing EMRI modeling accuracy.

Findings

First implementation of second-order self-force scheme

Calculation of gravitational binding energy for specific orbits

Enhanced accuracy for EMRI gravitational wave models

Abstract

Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.