On the Remote Sensing of Hawking Grey Pulses

The grey body radiation spectrum from various types of black holes is an interesting topic, both at the fundamental level and at the experimental (astrophysical) one. In a previous paper, I have applied the modified Moebius transform (henceforth MMT) due to Chen to the so-called distorted black holes, a terminology used by Geroch and Hartle to denote axially symmetric black hole Einstein solutions generated by Weyl’s technique from flat space Laplace equation. Here I provide some further details. In an astrophysical context, one expects quite naturally to encounter black holes carrying on an “external” distribution of matter. Examples are as follows (i) Weyl black holes, to which also Schwarzschild black holes belong. As is well-known the metric for a static axially symmetric spacetime in Weyl’s canonical coordinates (t, R, z, φ,) reads