# Naked singularity, firewall, and Hawking radiation

## TL;DR

This paper explores the nature of naked singularities and firewalls in black holes, demonstrating through analytical solutions that Hawking radiation and information preservation are consistent even in the presence of such singularities.

## Contribution

It provides vacuum solutions in $R^n$-gravity modeling firewall-type naked singularities and shows that Hawking radiation remains unitary and well-defined.

## Key findings

- Naked singularities modeled as firewall-type solutions in $R^n$-gravity.
- Hawking radiation remains thermal and preserves information.
- Surface gravity formula for temperature remains valid near naked singularities.

## Abstract

Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in $R^n$-gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by $2\pi$. This indicates that a naked singularity may not compromise the Hakwing evaporation process.

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Source: https://tomesphere.com/paper/1706.08850