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.