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Absorption Effects due to Spin in the Worldline Approach to Black Hole Dynamics

Rafael A. Porto

TL;DR

The paper extends the worldline EFT for black hole dynamics to incorporate spin by introducing spin-coupled quadrupole operators on the worldline and matching their correlators to graviton absorption in the low-frequency limit. It shows that superradiance drives the leading dissipative effect for spinning binaries, producing an enhancement of three powers of the relative velocity compared to the non-rotating case, with Kerr-specific cross sections containing a factor $(1+3 a_*^2)$. The framework is generalized to rotating neutron stars and to a test spinning black hole in a background spacetime, enabling predictions of absorption-powered energy loss based on internal structure or background curvature. The analysis leverages electric–magnetic duality to simplify the matching and suggests further work on higher-order corrections and finite-size effects within this dissipative, spin-dependent EFT approach.

Abstract

We generalize the effective point particle approach to black hole dynamics to include spin. In this approach dissipative effects are captured by degrees of freedom localized on the wordline. The absorptive properties of the black hole are determined by correlation functions which can be matched with the graviton absorption cross section in the long wavelength approximation. For rotating black holes, superradiance is responsible for the leading contribution. The effective theory is then used to predict the power loss due to spin in the dynamics of non-relativistic binary systems. An enhancement of three powers of the relative velocity is found with respect to the non-rotating case. Then we generalize the results to other type of constituents in the binary system, such as rotating neutron stars. Finally we compute the power loss absorbed by a test spinning black hole in a given spacetime background.

Absorption Effects due to Spin in the Worldline Approach to Black Hole Dynamics

TL;DR

The paper extends the worldline EFT for black hole dynamics to incorporate spin by introducing spin-coupled quadrupole operators on the worldline and matching their correlators to graviton absorption in the low-frequency limit. It shows that superradiance drives the leading dissipative effect for spinning binaries, producing an enhancement of three powers of the relative velocity compared to the non-rotating case, with Kerr-specific cross sections containing a factor . The framework is generalized to rotating neutron stars and to a test spinning black hole in a background spacetime, enabling predictions of absorption-powered energy loss based on internal structure or background curvature. The analysis leverages electric–magnetic duality to simplify the matching and suggests further work on higher-order corrections and finite-size effects within this dissipative, spin-dependent EFT approach.

Abstract

We generalize the effective point particle approach to black hole dynamics to include spin. In this approach dissipative effects are captured by degrees of freedom localized on the wordline. The absorptive properties of the black hole are determined by correlation functions which can be matched with the graviton absorption cross section in the long wavelength approximation. For rotating black holes, superradiance is responsible for the leading contribution. The effective theory is then used to predict the power loss due to spin in the dynamics of non-relativistic binary systems. An enhancement of three powers of the relative velocity is found with respect to the non-rotating case. Then we generalize the results to other type of constituents in the binary system, such as rotating neutron stars. Finally we compute the power loss absorbed by a test spinning black hole in a given spacetime background.

Paper Structure

This paper contains 5 sections, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Absorption effects for non--rotating binary Black Holes
  3. Absorption effects for spinning binary Black Holes
  4. A test spinning black hole in a background spacetime
  5. Conclusions

Figures (2)

  • Figure 1: Feynman diagram whose imaginary part gives the leading order contribution to the absorptive cross section. The dots correspond to insertions of leading multipole worldline operators.
  • Figure 2: Leading order contribution to the absorptive potential. The dots correspond to insertions of the leading worldline multipole operators.