Kerr退化阴影与旋转Hayward-like和Bardeen-like几何中的显著强偏折透镜效应
Kerr-Degenerate Shadows and Distinct Strong-Deflection Lensing in Rotating Hayward-like and Bardeen-like Geometries
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中文总结 AI 辅助
研究旋转Hayward-like和Bardeen-like正则黑洞的阴影与强偏折透镜，发现阴影与Kerr退化，但偏折量依赖正则长度，可用于区分不同几何。
中文摘要 AI 辅助
我们在一个共同的类Kerr轴对称ansatz下研究并比较旋转Hayward-like和Bardeen-like几何，这些模型通过其面积半径函数$R_i(\rho)$加以区分。在所采用的径向分支上，正的最小面积半径排除了Kerr环奇点位置，并且此处考察的曲率不变量保持有限。我们确定了包含两个、一个或零个视界的参数域。这两种几何具有相同的渐近Komar荷，但有限半径处的值不同。若将Einstein张量视为有效应力张量，则对于每个非零正则长度$\ell$，该ansatz违反零能量条件和弱能量条件，这通过赤道径向零收缩得以证明。对于黑洞分支上的完整光子族，其阴影边界与相同质量、自旋和观测者倾角下的Kerr阴影边界相同，并且对于这两种正则几何也相同。相应的M87*和Sgr A*的面积等效阴影直径与本文采用的基于事件视界望远镜（EHT）的近似区间一致，我们未获得对$\ell$的进一步约束。相反，顺行赤道强偏折极限（SDL）计算仅部分退化。在固定自旋下，$u_m^+$和$\theta_\infty^+$对Kerr和这两种正则几何是共同的，而$\bar a_+$、$\bar b_+$、图像分离度、相对星等以及次领头时间延迟修正依赖于$\ell$和面积半径轮廓。在所陈述的强偏折近似内，未来对$\Delta T_{2,1}$、$s^+$和$r_{\rm mag}^+$的测量可能有助于检验这些旋转几何，并将Hayward-like和Bardeen-like的预测与Kerr区分开来，包括在单视界参数域中，其中所采用的分支不包含类Kerr内视界。
英文摘要
We study and compare rotating Hayward-like and Bardeen-like geometries within a common Kerr-like axisymmetric ansatz, with the models distinguished by their areal-radius functions $R_i(ρ)$. On the adopted radial branches, the positive minimum areal radius excludes the Kerr ring locus, and the curvature invariants examined here remain finite. We identify the parameter domains containing two, one, or no horizons. The two geometries have the same asymptotic Komar charges but different finite-radius values. If we treat the Einstein tensor as an effective stress tensor, then for every nonzero regularity length $\ell$, this ansatz violates the null and weak energy conditions, as demonstrated by the equatorial radial-null contraction. For the complete photon family on a black-hole branch, the shadow boundary is identical to that of Kerr at the same mass, spin, and observer inclination, and is also identical for the two regular geometries. The corresponding area-equivalent shadow diameters for M87* and Sgr~A* are consistent with the approximate Event Horizon Telescope (EHT)-based intervals adopted here, and we do not obtain further constraints on $\ell$. By contrast, the prograde equatorial strong-deflection limit (SDL) calculations are only partly degenerate. At fixed spin, $u_m^+$ and $θ_\infty^+$ are common to Kerr and the two regular geometries, whereas $\bar a_+$, $\bar b_+$, the image separation, the relative magnitude, and the subleading time-delay correction depend on $\ell$ and on the areal-radius profile. Within the stated strong-deflection approximation, future measurements of $ΔT_{2,1}$, $s^+$, and $r_{\rm mag}^+$ may help test these rotating geometries and distinguish the Hayward-like and Bardeen-like predictions from Kerr, including in the one-horizon parameter domain where the adopted branch contains no Kerr-like inner horizon.
发表机构
- Fudan University（复旦大学）
- Hefei National Laboratory（合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
