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Causal Structure of Spacetime Singularities and Their Observable Signatures

Bina Patel, Jahnvi Mistry, Ayush Bidlan, Parth Bambhaniya

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.

Causal Structure of Spacetime Singularities and Their Observable Signatures

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 to null 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.
Paper Structure (8 sections, 60 equations, 6 figures, 2 tables)

This paper contains 8 sections, 60 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Causal structure of the JMN-1 spacetime
  3. Causal Structure of the JNW Spacetime
  4. Turning Points of Timelike Geodesics Near the JMN-1 Singularity
  5. Turning Points of Timelike Geodesics Near the JNW Singularity
  6. Tipler's Strength of JMN-1 and JNW Singularities
  7. Connection to EHT Imaging
  8. Discussion and Conclusions

Figures (6)

  • Figure 1: Schematic representation of the evolution of light-cone structures, highlighting the causal structure in the gravitational collapse of homogeneous dust.
  • Figure 2: Penrose diagram of Schwarzschild black hole.
  • Figure 3: This figure represents the light-cone structures and corresponding Penrose diagrams of the JMN-1 spacetime, with the singularity being timelike for $M_{0} < \frac{2}{3}$ and null for $M_{0} > \frac{2}{3}$. Here, $r=0$ represents the spacetime singularity and the total mass is considered as $M=1$.
  • Figure 4: This figure shows the light-cone structures and corresponding Penrose diagrams of the JNW spacetime, with the singularity being timelike for $0 < n < 1$, where $r=b$ represents the spherical singularity. The total mass is considered as $M=1$.
  • Figure 5: Angular momentum $L(r)$ required for radial turning points as a function of the radial coordinate $r$ for different values of the parameter $M_0$. The color bar indicates the corresponding values of $M_0$.
  • ...and 1 more figures