Relativistic Corrections to the Formation Rate of Extreme Mass-Ratio Inspirals

TL;DR

This paper develops a relativistic analytic model for estimating EMRI event rates, revealing that relativistic effects significantly increase predicted rates, especially for shallow stellar profiles, which is crucial for gravitational-wave detection planning.

Contribution

It introduces a relativistically self-consistent framework for EMRI rate estimation, extending the loss-cone theory to include general relativistic effects in Schwarzschild spacetime.

Findings

Relativistic effects increase EMRI rate predictions by about a factor of 8.

The rate enhancement is more significant for shallower stellar density profiles.

The predicted rates are insensitive to the mass of the central black hole.

Abstract

Extreme mass-ratio inspirals (EMRIs) are long-duration gravitational-wave sources in which a compact object gradually spirals into a massive black hole. Their formation is governed by the interplay between stochastic angular-momentum diffusion driven by two-body relaxation and the dissipative evolution caused by gravitational-wave emission, with the loss-cone boundary deciding whether an object undergoes an inspiral or a direct plunge. Building on this physical picture, we construct a relativistically self-consistent analytic framework for estimating EMRI event rates. In Schwarzschild spacetime, we generalize the standard loss-cone angular momentum to an energy-dependent quantity and revise the plunge pericenter by using the minimum stable radius derived from general relativity. Relative to the Newtonian treatment, we show that incorporating these relativistic effects increases the predicted EMRI rates by roughly a factor of 8. This enhancement becomes more pronounced for shallower stellar density profiles and is insensitive to the mass of the central massive black hole, which emphasizes that relativistic effects are essential for EMRI rate estimations that are relevant for space-based gravitational-wave detectors, such as LISA and Taiji.