Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse

TL;DR

This paper investigates electromagnetic radiation emitted during the formation of a naked singularity in a self-similar gravitational collapse, analyzing energy flux behavior and stability near the Cauchy horizon.

Contribution

It provides a new analytical framework using Green's functions to evaluate electromagnetic flux in self-similar collapse, clarifying mode contributions and divergence criteria.

Findings

Outgoing energy flux exhibits a power-law time evolution before singularity formation.

Criteria are established for divergence of flux at the Cauchy horizon.

Both quasi-normal modes and high-frequency waves are analyzed in the flux behavior.

Abstract

Dynamical evolution of test fields in background geometry with a naked singularity is an important problem relevant to the Cauchy horizon instability and the observational signatures different from black hole formation. In this paper we study electromagnetic perturbations generated by a given current distribution in collapsing matter under a spherically symmetric self-similar background. Using the Green's function method, we construct the formula to evaluate the outgoing energy flux observed at the future null infinity. The contributions from "quasi-normal" modes of the self-similar system as well as "high-frequency" waves are clarified. We find a characteristic power-law time evolution of the outgoing energy flux which appears just before naked singularity formation, and give the criteria as to whether or not the outgoing energy flux diverges at the future Cauchy horizon.