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

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-Cveti\v{c}-L\"u-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.