Classical Dressing of Timelike Naked Singularities

TL;DR

This paper explores conditions under which static, spherically symmetric matter distributions can cloak timelike naked singularities in general relativity, analyzing horizon formation through the matter profile and auxiliary functions.

Contribution

It introduces a formalism linking matter distribution properties to horizon formation, providing criteria for cloaking naked singularities in static spacetimes.

Findings

Non-negative, localized density profiles can cloak singularities when mass contributions are sufficient.

Monotonic profiles tend to produce a single outer horizon, while non-monotonic profiles can lead to multiple horizons.

The formalism is illustrated with various profiles, including power-law and logarithmic functions.

Abstract

We investigate whether a timelike naked singularity of negative-mass Schwarzschild type can be causally dressed by a static anisotropic matter distribution in classical general relativity. Working within a spherically symmetric framework, we solve Einstein's equations for a general density profile \(\rho(r)\) and show that the horizon structure is governed by the auxiliary function \(\Phi(r)=2m(r)-r\), whose zeros determine the existence and multiplicity of horizons. We derive sufficient conditions for the formation of a unique outer event horizon in terms of the total added mass, the localization of the matter profile, and the monotonic behavior of the effective compactness function \(8\pi r^2\rho(r)\). In particular, non-negative and sufficiently localized density profiles can cloak the timelike singularity when the cumulative matter contribution overcomes the negative bare mass, whereas non-monotonic profiles generically lead to multi-horizon geometries. We illustrate the formalism with discontinuous and smooth power-law profiles, logarithmic branches, and T-duality-inspired limiting configurations. These results provide a sufficient-condition framework for horizon formation around timelike naked singularities and clarify how the radial organization of matter controls causal accessibility in static general relativity.