Inferring black hole charge from backscattered electromagnetic radiation

We compute the scattering cross section of Reissner-Nordström 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 nonzero 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.

Figure 1

Electromagnetic scattering by Reissner-Nordström black holes for $q=0,0.8,1$ and $M\omega =0.5,1.0,2.0,3.0$. For $0<q\le 1$, the flux of EM radiation in the backward direction is nonzero; it diminishes as $M\omega$ increases.

Figure 2

Illustration of an electromagnetic-wave detection in the backward direction for a Schwarzschild (left) and an extreme Reissner-Nordström (right) black hole. Here, $M\omega =3.0$ and the scattering angle interval is between 172.6° and 180° in both graphs.