Causal Structure of Spacetime Singularities and Their Observable Signatures

TL;DR

This paper investigates the causal structures of specific horizonless compact objects, revealing how their singularities' nature affects photon trapping and observational signatures, with implications for astrophysical observations like black hole shadows.

Contribution

It provides a detailed analysis of the causal structure and geodesic behavior of JMN-1 and JNW spacetimes, linking singularity types to observable lensing and shadow features.

Findings

JMN-1 transitions from timelike to null singularity

JNW remains timelike singularity throughout

Photon spheres exist in Schwarzschild and JNW, but only in null phase of JMN-1

Abstract

We analyze the causal structure of horizonless compact objects via the light-cone geometry and conformal compactification of the Joshi-Malafarina-Narayan (JMN-1) and Janis-Newman-Winicour (JNW) spacetimes. Penrose diagrams reveal that JMN-1 undergoes a transition from timelike $(0<M_0<2/3)$ to null $(2/3<M_0<4/5)$ singularities, while JNW remains timelike throughout, in contrast to the spacelike singularity of the Schwarzschild spacetime. We show that photon spheres exist in Schwarzschild and JNW, but arise in JMN-1 only in the null singularity phase, establishing a direct link between causal character and null geodesic trapping. We further demonstrate that radial timelike geodesics develop turning points for certain parameter regimes in both JMN-1 and JNW spacetimes, indicating the emergence of effective repulsive behavior in the strong field region. These features lead to distinct strong field lensing and shadow signatures, potentially testable by very long baseline interferometric observations such as those of the Event Horizon Telescope.