发表机构
Physics Department, California State University, Fresno（弗雷斯诺加州州立大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一族由核心指数、正则化尺度和形变参数描述的正则黑洞，系统分析其热力学与测地线性质，为研究可调核心和类RN形变的影响提供统一框架。
AI 中文摘要
我们引入了一族静态且球对称的正则黑洞几何，其特征由离散的核心指数$n$、正则化尺度$a$和无量纲形变参数$\eta$描述。该构造始于一个具有可调中心行为的正定归一化有效密度分布。最低阶成员以巴丁几何作为极限情形，而非零形变参数则产生类赖斯纳-诺德斯特伦渐近修正。参数$n$控制中心耗尽的阶数：最低阶成员具有德西特型核心，而更高阶成员则趋近于具有消失密度和曲率的类闵可夫斯基中心。我们确定了视界结构、极端条件、霍金温度、熵以及由径向爱因斯坦方程隐含的视界热力学恒等式。通过分析零测地线，我们获得了光子球、临界碰撞参数和阴影半径，包括解析弱形变近似、精确的史瓦西和巴丁极限，以及与主导的类赖斯纳-诺德斯特伦行为的比较。随后，利用光子轨道角频率和李雅普诺夫指数来分离轨道时间尺度和不稳定性时间尺度；它们的比值提供了阴影半径中尚未包含的信息。通过渐近度量的受控扇区隔离展开，我们讨论了弱引力透镜和放大效应。我们进一步研究了类时测地线、圆周运动、边际束缚轨道和最内层稳定圆轨道，推导出精确隐式关系和微扰表达式。该模型为研究可调正则核心和类RN外部形变如何影响正则黑洞的热力学和测地线性质提供了一个统一框架。
英文摘要
We introduce a family of static and spherically symmetric regular black-hole geometries characterized by a discrete core index $n$, a regularization scale $a$, and a dimensionless deformation parameter $η$. The construction starts from a positive, normalized effective density profile with a tunable central behavior. The lowest member contains the Bardeen geometry as a limiting case, whereas a nonzero deformation parameter generates a Reissner--Nordström-like asymptotic correction. The parameter $n$ controls the order of central depletion: the lowest member possesses a de Sitter-type core, whereas higher members approach a Minkowski-like center with vanishing density and curvature. We determine the horizon structure, extremality condition, Hawking temperature, entropy, and the horizon thermodynamic identity implied by the radial Einstein equation. Null geodesics are analyzed to obtain the photon sphere, critical impact parameter, and shadow radius, including analytic weak-deformation approximations, the exact Schwarzschild and Bardeen limits, and comparison with the leading Reissner--Nordström-like behavior. The photon-orbit angular frequency and Lyapunov exponent are then used to separate orbital and instability timescales; their ratio provides information not already contained in the shadow radius. Weak gravitational lensing and magnification are discussed through a controlled sector-isolated expansion of the asymptotic metric. We further study timelike geodesics, circular motion, the marginally bound orbit, and the innermost stable circular orbit, deriving exact implicit relations and perturbative expressions. The model provides a unified framework for investigating how a tunable regular core and an RN-like exterior deformation affect the thermodynamic and geodesic properties of regular black holes.
