Moebius Inverse Problem for Distorted Black Holes

TL;DR

This paper explores using a modified Möbius transform to solve the inverse black body problem for detecting and analyzing distorted micro-black holes through their Hawking radiation signals.

Contribution

It applies the modified Möbius transform to Hawking radiation data to determine the temperature distribution of distorted micro-black holes, extending previous inverse black body problem solutions.

Findings

Successful application of Möbius transform to Hawking radiation data

Potential to identify matter distribution around micro-black holes

Insights into supersymmetric applications of Möbius functions

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.