On arithmetic detection of grey pulses with application to Hawking radiation

TL;DR

This paper proposes a novel mathematical approach using a Ramanujan generalization of the Moebius inverse transform to analyze Hawking radiation spectra from small black holes, aiding in remote temperature distribution detection.

Contribution

It introduces a new wavelet-based method based on Ramanujan sums for analyzing grey pulses in Hawking radiation spectra, extending previous inverse transform techniques.

Findings

New Ramanujan-based inverse transform for grey pulse analysis

Potential application to black hole temperature mapping

Enhanced spectral analysis method for Hawking radiation

Abstract

Micron-sized black holes do not necessarily have a constant horizon temperature distribution. The black hole remote-sensing problem means to find out the `surface' temperature distribution of a small black hole from the spectral measurement of its (Hawking) grey pulse. This problem has been previously considered by Rosu, who used Chen's modified Moebius inverse transform. Here, we hint on a Ramanujan generalization of Chen's modified Moebius inverse transform that may be considered as a special wavelet processing of the remote-sensed grey signal coming from a black hole or any other distant grey source