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<p>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 <b>𝔤</b>. 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 <i>d</i> + 1 spacetime dimensions, its gyromagnetic factor is equal to <b>𝔤</b> = (<i>d</i> − 1)/(<i>d</i> − 2). Hence, only in 3 + 1 dimensions minimal coupling is sufficient to describe black holes from scattering amplitudes.</p>

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

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  • 发表日期：

    2026年3月11日

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  • Claudio Gambino,
  • Fabio Riccioni,
  • Victor Sanz Sanchis

摘要

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 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 𝔤 = (d − 1)/(d − 2). Hence, only in 3 + 1 dimensions minimal coupling is sufficient to describe black holes from scattering amplitudes.