The gyromagnetic factor of charged rotating black holes in various dimensions from scattering amplitudes

TL;DR

The paper addresses constructing the exterior fields of charged, rotating black holes in arbitrary dimensions by matching the classical limit of quantum scattering amplitudes in a gravity EFT at first post-Minkowskian order and dipole accuracy. It develops the metric and electromagnetic potential from graviton/photon emission amplitudes, introducing a Pauli non-minimal coupling that encodes the gyromagnetic factor $\mathfrak{g}$ and, in five dimensions, a Chern-Simons term that affects the vector potential. It reproduces Kerr-Newman in $3+1$ dimensions with minimal coupling and the Chong-Cvetič-Lü-Pope solution in $4+1$ dimensions with a Pauli term giving $\mathfrak{g}=\tfrac{3}{2}$ and $\lambda=1$, and proves a universal higher-dimensional gyromagnetic factor for charged Myers-Perry–like BHs, with $\mathfrak{g}_{\mathrm{BH}}=\frac{d-1}{d-2}$, with $\zeta=-(d-3)/(2(d-2))$. This work clarifies when non-minimal couplings are required in the amplitude description of BHs and sets the stage for higher-order multipoles and extensions to other dimensions and interactions.

Abstract

Classical black hole spacetimes can be recovered from the classical limit of quantum scattering amplitudes in a low-energy effective field theory of gravity. In this work we compute, at first post-Minkowskian and dipole order, the metric and the electromagnetic potential for charged and rotating black holes in general spacetime dimensions from amplitudes describing the emission of either a graviton or a photon from a massive and charged Dirac fermion field up to one loop. In addition, we introduce a Pauli non-minimal coupling, to parametrize the black hole's gyromagnetic factor $\mathfrak{g}$. We are able to reproduce the Kerr-Newman solution in four dimensions, as well as the Chong-Cvetič-Lü-Pope solution, from five-dimensional supergravity, which includes a Chern-Simons interaction. Crucially, we show that for a charged Myers-Perry like black hole in $d+1$ spacetime dimensions, its gyromagnetic factor is equal to $\mathfrak{g}=(d-1)/(d-2)$. Hence, only in $3+1$ dimensions minimal coupling is sufficient to describe black holes from scattering amplitudes.

Figures (3)

• Figure 1: Diagrams, with corresponding multiplicity, employed for the computation of the PM expansion of the metric up to 1PM and in dipole approximation. The fermion-fermion squared vertex represents the Pauli coupling.
• Figure 2: Diagrams, with corresponding multiplicity, used in the calculation of the PM expansion of the potential up to 1PM, linear in the charge and in dipole approximation. The fermion-fermion squared vertex represents the Pauli coupling.
• Figure 3: Diagrams including the Chern-Simons interaction (the 3-photon squared vertex) with the corresponding multiplicity, inserted in five dimensions to compute up to one-loop and 1PM in dipole approximation.