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Spin-1 Amplitudes in Black-Hole Evaporation

A. N. St. J. Farley·P. D. D'Eath
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Abstract

Our earlier work on the quantum amplitude for a scalar field in black-hole evaporation, following gravitational collapse, is here extended to Maxwell theory. Boundary data are specified on initial and final space-like hypersurfaces $Σ_{I,F}$, separated by a large Lorentzian proper-time interval $T$, as measured at spatial infinity. The initial boundary data may be chosen (say) to be spherically symmetric, corresponding to a nearly-spherical configuration prior to gravitational collapse. The final data include the intrinsic 3-metric and scalar field, restricted to $Σ_F$, in addition to spin-1 data, naturally taken to be the magnetic field $B_i$ on $Σ_{I,F} (i=1,2,3)$. For a locally-supersymmetric theory, the quantum amplitude should be proportional to $\exp(iS_{\rm class})$, apart from corrections which are very small when the frequencies in the boundary data are small compared to the Planck scale. Here, $S_{\rm class}$ is the action of the classical solution. The Lorentzian amplitude is found by taking the limit $θ\to 0_+$. By a method similar to that used in the spin-0 case, one obtains the quantum amplitude for photon data on $Σ_F$. The magnetic boundary conditions are related by supersymmetry to the natural spin-2 (gravitational-wave) boundary conditions, which involve fixing the magnetic part of the Weyl tensor.

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A. N. St. J. Farley, P. D. D'Eath. 2005-10-07. Spin-1 Amplitudes in Black-Hole Evaporation. https://doi.org/10.1088/0264-9381%2F22%2F14%2F010

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