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Linking interior curvature to observable shadows: A case study of nonsingular black holes

Ming-Xin Li, Jin Pu, Yi Ling, Guo-Ping Li

Abstract

We establish a direct connection between the interior curvature structure of nonsingular black holes (BHs) with a Minkowski core and their observable optical signatures. By classifying these spacetimes into three fundamental types, Type I (Kretschmann scalar K_max increasing with mass M), Type II (mass-independent K_max), and Type III (K_max decreasing with M), we demonstrate how subtle variations in the core geometry imprint distinguishable features on the BH shadow. A detailed analysis of photon dynamics reveals that the parameters α and n, which control the deviation from Schwarzschild geometry and the radial decay of the regularizing factor, respectively, systematically alter the properties of the photon sphere. These intrinsic geometric differences propagate outward: for fixed parameters, Type III BHs, with the most compact photon sphere, produce the smallest and brightest shadows, whereas Type I BHs yield the largest and dimmest ones. Shadow computations under both static and infalling spherical accretion models confirm that the curvature-based classification directly corresponds to observable differences. Critically, Type III BHs exhibit the strongest sensitivity to parameter variations, making them optimal probes for constraining the underlying spacetime geometry. Our work reveals that even among nonsingular BHs sharing the same asymptotic core, differences in internal curvature are reflected in the shadow morphology, thereby providing a new pathway to test quantum-gravity-inspired models using upcoming high-resolution observations.

Linking interior curvature to observable shadows: A case study of nonsingular black holes

Abstract

We establish a direct connection between the interior curvature structure of nonsingular black holes (BHs) with a Minkowski core and their observable optical signatures. By classifying these spacetimes into three fundamental types, Type I (Kretschmann scalar K_max increasing with mass M), Type II (mass-independent K_max), and Type III (K_max decreasing with M), we demonstrate how subtle variations in the core geometry imprint distinguishable features on the BH shadow. A detailed analysis of photon dynamics reveals that the parameters α and n, which control the deviation from Schwarzschild geometry and the radial decay of the regularizing factor, respectively, systematically alter the properties of the photon sphere. These intrinsic geometric differences propagate outward: for fixed parameters, Type III BHs, with the most compact photon sphere, produce the smallest and brightest shadows, whereas Type I BHs yield the largest and dimmest ones. Shadow computations under both static and infalling spherical accretion models confirm that the curvature-based classification directly corresponds to observable differences. Critically, Type III BHs exhibit the strongest sensitivity to parameter variations, making them optimal probes for constraining the underlying spacetime geometry. Our work reveals that even among nonsingular BHs sharing the same asymptotic core, differences in internal curvature are reflected in the shadow morphology, thereby providing a new pathway to test quantum-gravity-inspired models using upcoming high-resolution observations.
Paper Structure (9 sections, 27 equations, 12 figures)

This paper contains 9 sections, 27 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Spacetime geometry and curvature classification
  3. Metric and curvature-based classification
  4. Photon sphere and effective potential
  5. Orbit classification and critical parameters
  6. Optical appearance and shadow formation
  7. Static spherical accretion model
  8. Infalling spherical accretion model
  9. Conclusions and discussions

Figures (12)

  • Figure 1: The Kretschmann scalar $K$ as a function of $r$ for the three types of nonsingular BHs with a Minkowski core.
  • Figure 2: Dependence of the Kretschmann scalar $K$ on $\alpha$ for the three BH types ($n=2$, $M=2$).
  • Figure 3: Dependence of $K(r)$ on $n$ for the three BH types ($M=2$, $\alpha=0.7$).
  • Figure 4: Maximum Kretschmann scalar $K_{\max}$ as a function of $\beta$ for Type I and III BHs ($\alpha=0.7$).
  • Figure 5: Effective potential $V_{\text{eff}}(r)$ for three BH types at different values of $n$ ($M=2$, $\alpha=0.7$).
  • ...and 7 more figures