迪姆尼科娃黑洞的潮汐力
Dymnikova Black Hole Tidal Forces
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- Universidade Federal do Ceará (UFC)（塞阿拉联邦大学）
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中文总结 AI 辅助
本研究探究迪姆尼科娃正则黑洞的潮汐力性质，推导相关测地线与潮汐张量方程，发现其潮汐力在内区保持有限，德西特核可正则化延展下落天体的潮汐动力学。
中文摘要 AI 辅助
本研究探讨迪姆尼科娃正则黑洞的潮汐性质及其对径向自由下落大质量粒子的影响。从迪姆尼科娃静态球对称解出发，推导类时径向测地线方程，构建适配自由下落观测者的正交归一标架；进而得到潮汐张量的径向与角向分量，分析其对黑洞质量及德西特核特征长度尺度的依赖关系。在大径向距离处，潮汐力恢复史瓦西行为；而在正则中心附近，两个分量均保持有限，体现时空的非奇异性。研究表明，径向与角向潮汐力在事件视界内的特征半径处消失并变号，指示拉伸与压缩状态间的转变；从事件视界外静止释放的粒子会到达柯西视界内的折返点，而非正则中心。此外，针对两组初始条件求解测地线偏离方程，考察偏离矢量的径向与横向分量演化，发现解渐近复现史瓦西行为，但在内区差异显著：偏离矢量分量在折返点前保持有限，而史瓦西情形下对应径向分量在奇点处发散。这些结果揭示了德西特核如何正则化延展下落天体的潮汐动力学。
英文摘要
In this work we investigate the tidal properties of the Dymnikova regular black hole and their ef fects on massive particles in radial free-fall. Starting from Dymnikova static, spherically symmetric solution, we derive the equations governing timelike radial geodesics and construct an orthonormal tetrad adapted to a free-falling observer. We then obtain the radial and angular components of the tidal tensor and analyze their dependence on the black hole mass and the characteristic length scale of the de Sitter core. At large radial distances, tidal forces recover Schwarzschild behavior, whereas near the regular center, both components remain finite, reflecting the non-singular nature of the spacetime. We show that the radial and angular tidal forces vanish and change sign at characteris tic radii inside the event horizon, indicating transitions between stretching and compression regimes. A particle released from rest outside the event horizon reaches a turnaround point located inside the Cauchy horizon, rather than reaching the regular center. We also solve the geodesic deviation equations for two sets of initial conditions and examine the evolution of the radial and transverse components of the deviation vector. Although the solutions asymptotically reproduce Schwarzschild behavior, they differ significantly in the inner region: the deviation vector components remain finite up to the turnaround point, whereas the corresponding radial component in the Schwarzschild case diverges at the singularity. These results demonstrate how the de Sitter core regularizes the tidal dynamics of extended falling bodies.
