Moebius Inverse Problem for Distorted Black Holes

Abstract

Hawking ``thermal'' radiation could be a means to detect black holes of micron sizes, which may be hovering through the universe. We consider these micro-black holes to be distorted by the presence of some distribution of matter representing a convolution factor for their Hawking radiation. One may hope to determine from their Hawking signals the temperature distribution of their material shells by the inverse black body problem. In 1990, Nan-xian Chen has used a so-called modified M\"{o}bius transform to solve the inverse black body problem. We discuss and apply this technique to Hawking radiation of distorted micro-black holes. Some comments on supersymmetric applications of M\"{o}bius function and transform are also added.