Classical Dressing of Timelike Naked Singularities

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 \(ρ(r)\) and show that the horizon structure is governed by the auxiliary function \(Φ(r)=2m(r)-r\), 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 \(8πr^2ρ(r)\). 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.