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

Chen Feng; Yong Tang

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arXiv · 2603.09547

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

Chen Feng·Yong Tang

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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.

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Chen Feng, Yong Tang. 2026-03-10. Relativistic Corrections to the Formation Rate of Extreme Mass-Ratio Inspirals. https://arxiv.org/abs/2603.09547

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