来自非线性电动力学和T对偶启发的零点长度的双尺度带磁荷正则黑洞
Two-scale magnetically charged regular black holes from nonlinear electrodynamics and a T-duality-inspired zero-point length
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中文总结 AI 辅助
本研究基于非线性电动力学和T对偶启发的零点长度构建双尺度带磁荷正则黑洞，推导其热力学、光学及弱场修正性质，并结合等离子体模型得到阴影的精确参数关系。
中文摘要 AI 辅助
我们在爱因斯坦引力中构建了一种双尺度、静态球对称的正则黑洞，其源为磁性非线性电动力学（NED，nonlinear electrodynamics）。零点长度$\boldsymbol{\u2113}$对质量和电荷分布进行正则化，而$\boldsymbol{q}$为渐近磁荷。该几何在大半径处趋近于Reissner-Nordström（雷斯勒-诺德斯特洛姆）解，当$q=0$时退化为中性零点长度解，当$\u2113=|q|$时几何上与Ayón-Beato-García解一致。对于$q\neq0$的情况，逆重构得到具有麦克斯韦渐近行为且强场极限有限的单值磁拉格朗日量。黑洞中心是正则的，根据$2M\u2113-q^2$的符号分别为de Sitter（德西特）空间、局部闵可夫斯基空间或anti-de Sitter（反德西特）空间；当且仅当$3M\u2113\boldsymbol{\u2265}2q^2$时，弱能量条件全局成立。我们推导了极值曲线、精确热容量，以及在保留Wald面积熵的前提下的齐次视界变分恒等式和Smarr恒等式。我们还证明，该族中的每一个带电黑洞在外通讯域内都具有非简并的超常NED光学度规。相关的捕获阴影由光学碰撞参数函数的全局最小值决定，通常与背景测地线阴影不同。弱场计算给出了近心点、光线偏折、时间延迟和红移的修正；特别地，$\u2113$首次出现在标准后牛顿一阶参数之外的阶次中。最后，针对冷透明等离子体中的最小耦合测试辐射，我们得到了幂律密度分布下的精确参数化阴影关系，并将哈密顿射线追踪与Novikov-Thorne盘模型相结合。我们仅将一种单独的超常NED-等离子体延拓作为唯象方案给出，因为物质等离子体会打破真空特征度规的共形模糊性。
英文摘要
We construct a two-scale, static, spherically symmetric regular black hole in Einstein gravity sourced by magnetic nonlinear electrodynamics (NED). The zero-point length $\ell$ regularizes the mass and charge profiles, whereas $q$ is the asymptotic magnetic charge. The geometry approaches Reissner-Nordström at large radius, reduces to the neutral zero-point-length solution for $q=0$, and coincides geometrically with the Ayón-Beato-García solution for $\ell=|q|$. For $q\neq0$, inverse reconstruction gives a single-valued magnetic Lagrangian with Maxwell asymptotics and a finite strong-field limit. The center is regular and is de Sitter, locally Minkowski, or anti-de Sitter according to the sign of $2M\ell-q^2$; the weak energy condition holds globally if and only if $3M\ell\geq2q^2$. We derive the extremality curve, the exact heat capacity, and homogeneous horizon-variation and Smarr identities while retaining the Wald area entropy. We also prove that every charged black hole in this family has a nondegenerate extraordinary NED optical metric throughout the domain of outer communication. The associated capture shadow is selected by the global minimum of the optical impact-parameter function and generally differs from the background-geodesic shadow. Weak-field calculations yield the periapsis, bending, time-delay, and redshift corrections; in particular, $\ell$ first appears beyond the standard first-post-Newtonian parameters. Finally, for minimally coupled test radiation in a cold transparent plasma, we obtain exact parametric shadow relations for power-law density profiles and combine Hamiltonian ray tracing with a Novikov-Thorne disk model. A separate extraordinary NED-plasma continuation is displayed only as a phenomenological prescription because a material plasma breaks the conformal ambiguity of the vacuum characteristic metric.
