Generalized JMN Naked Singularity Models

TL;DR

This paper introduces a generalized class of JMN naked singularity models with inhomogeneous density profiles, analyzing their observational signatures and showing they closely resemble Schwarzschild black holes in shadow and accretion features.

Contribution

The paper extends JMN models by incorporating density inhomogeneity, providing a two-parameter family of solutions and examining their observational implications.

Findings

Shadow profiles are identical to Schwarzschild when the photon sphere is outside the singularity.

Accretion spectra show increased high-frequency emission compared to Schwarzschild.

Deviations from original JMN models are minimal due to strong inhomogeneity constraints.

Abstract

We construct a generalized class of Joshi-Malafarina-Narayan (JMN) naked singularity spacetimes that arise as equilibrium end states of gravitational collapse with non-vanishing tangential pressure. The generalization introduces density inhomogeneity through a radially dependent mass function $F(r)=(M_0+M_n r^n)r^3$, leading to a two-parameter family of solutions matched smoothly to an exterior Schwarzschild spacetime. The observational properties of the spacetime are then examined through shadow formation and thin accretion disk emission. We find that when the photon sphere lies in the exterior Schwarzschild region, the shadow is identical to that of a Schwarzschild black hole. Accretion disk spectra show enhanced high-frequency emission compared to Schwarzschild, while deviations from the original JMN model remain small due to strong constraints on the inhomogeneity parameter. These results indicate that the generalized model effectively serves as a small perturbation of the JMN spacetime, demonstrating the robustness of JMN-type naked-singularity geometries.