Non-conservative effects on Spinning Black Holes from World-Line Effective Field Theory

TL;DR

This paper develops and applies a worldline EFT framework to compute non-conservative, dissipative tidal effects on spinning Kerr black holes across all spins in the long-wavelength regime. By matching to low-energy graviton absorption, it derives the Wightman and retarded Green's functions governing horizon dissipation, and shows static Love numbers vanish, while dissipative responses lead to tidal heating and angular momentum exchange. It reports novel Post-Newtonian results for binary dynamics: a 5PN non-conservative force, a 4PN torque, and a 2.5PN energy transfer between horizon and orbit, with implications for gravitational-wave modeling and the Penrose process. The work provides a systematic, spin-agnostic approach that can be extended to higher-order corrections and helps reconcile previous results in the literature.

Abstract

We generalize the worldline EFT formalism developed in [4-9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process.

Figures (1)

• Figure 1: Potential exchange diagrams that contribute to the two-particle action $S_{int}$. In (a) the particles interact through the minimal gravitational interaction. Figure (b) is the term in $S_{int}$ generated by the quadrupole couplings of particle 1 (a similar diagram with $1\leftrightarrow 2$ has been omitted).