Inferring black hole charge from backscattered electromagnetic radiation

Understand

We compute the scattering cross section of Reissner-Nordstr\"om black holes for the case of an incident electromagnetic wave.

• We describe how scattering is affected by both the conversion of electromagnetic to gravitational radiation, and the parity-dependence of phase shifts induced by the black hole charge.
• The latter effect creates a helicity-reversed scattering amplitude that is non-zero in the backward direction.
• We show that from the character of the electromagnetic wave scattered in the backward direction it is possible, in principle, to infer if a static black hole is charged.