[论文解读] Breaking the degeneracy among regular black holes with gravitational lensing

Hong Liu, Xiaolong Liao+1 more|arXiv (Cornell University)|Mar 21, 2026

Astrophysical Phenomena and Observations被引用 0

一句话总结

该论文利用弱透镜/强透镜、阴影和准正规模来分析 Culetu、Bardeen 与 Hayward 正则黑洞之间的参量简并性，并提出高阶观测量以打破简并。

ABSTRACT

We examine parameter degeneracies in Culetu, Bardeen and Hayward regular black holes across lensing, shadow and quasinormal mode regimes. Our analysis reveals that while Einstein ring data yield extremely loose constraints, with the regularization parameter $q$ exceeding $\mathcal{O}(10^3)$, they fail to improve the parameter estimation when combined with strong lensing observables. In contrast, the Event Horizon Telescope observations provide remarkably tight limits: $0 \leq q < 0.0466 <0.0847$ for Culetu, $0 \leq q < 0.5115 <0.6682$ for Bardeen and $0 \leq q < 1.0258 <1.1881$ for Hayward, which shows that the strong field regime alone dominates the available parameter space. Despite these bounds, leading order geometric observables remain highly degenerate, which masks the microscopic details of non-singular cores. To break this ``macroscopic universality,'' we identify high order signatures, such as the Lyapunov exponent and subleading time delays, as sensitive probes of near horizon curvature. Crucially, we discover that the brightness hierarchy of accretion induced intensity profiles undergoes a fundamental inversion when transitioning from lensing dominated static flows to dynamics dominated infalling flows. These results demonstrate that high resolution temporal and intensity profiles are essential for distinguishing between regular black hole geometries.

研究动机与目标

• Motivate testing regular black hole interiors as alternatives to singular Schwarzschild black holes.
• Unify Culetu, Bardeen, and Hayward RBH frameworks under the Fan–Wang class and study their observational signatures.
• Quantify parameter constraints from weak (Einstein ring) and strong (shadow) lensing and compare with EHT data.
• Identify degeneracies in macroscopic observables and propose higher-order probes to distinguish core structures.
• Discuss implications for future high-resolution timing and intensity measurements of accretion flows.

提出的方法

• Adopt the generalized Fan–Wang RBH metric A(r)=1-2Mr^2/(r^ν+ρ^ν)^{μ/ν} with μ=3 and dimensionless form A(x)=1-2x^2/(x^ν+q^ν)^{3/ν}.
• Compute photon sphere x_m and critical impact parameter b_m from Bozza formalism for strong deflection lensing.
• Derive Einstein ring angle θ_E from weak lensing and compare with ESO325-G004 data.
• Perform χ^2 analysis using shadow observables θ_d (and θ_∞) from M87* and Sgr A* to constrain q for Culetu, Bardeen, and Hayward RBHs.
• Analyze higher-order strong-lensing coefficients (ā, b̄), time delays ΔT with subleading corrections, and Lyapunov exponent λ as higher-order probes.
• Examine shadows with static and infalling spherical accretion flows and study intensity profiles I(b) as a function of q.

Figure 1: The angular radius of Einstein ring $\theta_{E}$ as functions of parameter $q$ and the $\chi^{2}$ test results for Culetu, Bardeen and Hayward black holes. In left one, the data from galaxy ESO325-G004 are $\theta_{E}^{\rm obs}=2.85^{+0.55}_{-0.25}as$ [ 89 , 28 ] . The black dashed line de

实验结果

研究问题

• RQ1 What ranges of the regularization parameter q are allowed for Culetu, Bardeen, and Hayward RBHs under current lensing/shadow observations?
• RQ2 Do strong-field observables (shadow size, photon sphere characteristics) exhibit degeneracies among these RBHs, and if so, can higher-order lensing/dynamical signatures lift them?
• RQ3 How do static versus infalling accretion flows affect the observed shadow and brightness profiles for these RBHs?
• RQ4 Which observables beyond the leading order (e.g., subleading time delays, Loupian coefficients) are most effective at distinguishing RBH interiors?

主要发现

BH types	Parameters	Einstein ring constraints	Strong lensing constraints	Joint lensing constraints
Culetu BH	q	0.7978×10^3	0.0466	0.0466
Culetu BH	q	1.0413×10^3	0.0847	0.0847
Bardeen BH	q	5.4340×10^4	0.5115	0.5115
Bardeen BH	q	7.9982×10^4	0.6682	0.6682
Hayward BH	q	1.3560×10^5	1.0258	1.0258
Hayward BH	q	1.7546×10^5	1.1881	1.1881

• Strong lensing (shadow) data from EHT tightly constrain q: Culetu 0≤q<0.0466<0.0847, Bardeen 0≤q<0.5115<0.6682, Hayward 0≤q<1.0258<1.1881.
• Einstein ring data yield loose constraints (q≈O(10^3)–O(10^5)) and do not significantly improve parameter estimation when combined with strong lensing.
• Leading-order observables (shadow radius, b_m) are highly degenerate across the three RBH models due to Schwarzschild-like asymptotics, masking core differences.
• Higher-order strong-lensing coefficients (ā, b̄) and subleading time delays (ΔT^1_{n,m}) show model-dependent behavior and can help break degeneracy (Culetu vs Bardeen/Hayward).
• Lyapunov exponent λ and QNM frequencies Ω_m track changes in q and differ among models, offering additional discriminants.
• Shadows with static vs infalling accretion flows reveal a brightness hierarchy that can invert between regimes, highlighting the importance of high-resolution timing/intensity data for distinguishing RBHs.

Figure 3: Same as Fig. 2 , but for the angular observable $\theta_{d}/\mu as(\theta_{\infty}/\mu as)$ , shadow area $\tilde{A}/M^{2}$ , time delay leading order term $\Delta T^{0}_{n,m}$ and QNM frequency $\Omega_{m}$ .