Graviton-Photon Mixing by a Kerr-Newman Black Hole with Worldline EFT

TL;DR

This paper develops a worldline EFT framework to study graviton–photon mixing mediated by a spinning charged Kerr–Newman black hole in the long-wavelength limit. By matching worldline Wilson coefficients to the KN multipole structure, the authors derive gauge-invariant tree-level amplitudes for graviton→photon conversion up to $\mathcal{O}((\omega/m)^2)$ and $\mathcal{O}(S^2)$, and compute the full angular dependence of the conversion cross section, including spin effects. They show a factorization between the graviton photoproduction amplitude and the photon Compton amplitude at zeroth order in spin, but this breaks when spin is turned on, highlighting differences between classical and quantum spinning sources. The results provide a concrete benchmark for future analyses of coupled gravitoelectromagnetic scattering in spinning charged backgrounds and offer insights into how spin-induced multipoles shape cross sections in these mixed gauge sectors.

Abstract

In black hole perturbation theory, the difficulty in separating electromagnetic and gravitational sectors of the coupled Teukolsky equations has prevented a general treatment of scattering processes involving both electromagnetic waves and gravitational waves in presence of a Kerr-Newman black hole. We present the first computation of the gauge-invariant, low-frequency scattering amplitude for graviton photoproduction by a Kerr-Newman black hole at tree level up to $\mathcal{O}\big((ω/m)^2\big)$ or $\mathcal{O}(S^2)$ and linear in $κ$, using the worldline effective field theory. The relevant Wilson coefficients are determined by matching the graviton and photon one-point functions to the Kerr-Newman solution. We obtain the full angular dependence of the conversion cross section in the presence of spin and comment on the factorization relation between the graviton photoproduction amplitude and the photon Compton amplitude for a classical spinning source. The result provides a benchmark for future analyses of coupled gravitoelectromagnetic scattering in spinning charged compact object backgrounds.

Figures (4)

• Figure 1: Unpolarized differential cross sections of graviton photoproduction. Left: the incoming graviton's momentum is aligned with the spin, $\alpha=0, \theta=0$. Middle: the incoming graviton's momentum is orthogonal to the spin, $\alpha=0, \theta=\pi$. Right: the incoming graviton's momentum is orthogonal to the spin, $\alpha=0, \theta=\pi/2$.
• Figure 2: Spin correction in the unpolarized differential cross sections of graviton photoproduction. For graviton-spin alignment/anti-alignment, the spin dependence drops out. Here we present the spin corrections for (1)$\alpha=0, \theta=\pi/3$, (2)$\alpha=0, \theta=\pi/2$, (3)$\alpha=0, \theta=2\pi/3$.
• Figure 3: Spin correction to the differential cross sections of graviton photoproduction in the "++" channel. For graviton-spin alignment/anti-alignment, the spin dependence drops out. Here we present the spin corrections for (1)$\alpha=0, \theta=0$, (2)$\alpha=0, \theta=\pi/3$, (3)$\alpha=0, \theta=\pi/2$.
• Figure 4: Spin correction to the differential cross sections of graviton photoproduction in the "+--" channel. For graviton-spin alignment/anti-alignment, the spin dependence drops out. Here we present the spin corrections for (1)$\alpha=0, \theta=0$, (2)$\alpha=0, \theta=\pi/3$, (3)$\alpha=0, \theta=\pi/2$.