Kalb-Ramond黑洞中的零测地线及其稳定性研究
Study of Null Geodesics and their Stability in Kalb-Ramond Black Holes
- Universidad Diego Portales（迭戈·波塔莱斯大学）
- National Technical University of Athens（雅典国立技术大学）
- Universidad de La Serena（拉塞雷纳大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究Kalb-Ramond黑洞中零测地线及其稳定性，发现洛伦兹破缺参数和宇宙学常数分别以不同方式改变光子球不稳定性，零测地线可作为洛伦兹破缺效应的敏感探针。
AI中文摘要：
我们研究了带宇宙学常数的四维带电Kalb-Ramond黑洞中的零测地线及其稳定性。背景反对称张量场的非零真空期望值诱导了自发洛伦兹对称性破缺，该破缺由无量纲参数$l$控制，并使Reissner-Nordström-(A)dS几何发生形变。我们推导了无质量粒子的有效势，并获得了光子球半径、临界碰撞参数、俘获截面和偏转轨迹的解析表达式。极限情形$l\ ightarrow0$恢复了RN、RN-dS和RN-AdS的测地线结构，而有限的$l$值会移动转折点、改变光的偏转并使第一类和第二类光子轨迹发生形变。在AdS分支中，我们发现了一种特殊的极限型limaçon零测地线，其角结构受Kalb-Ramond参数修正。我们还计算了不稳定圆形零轨道的Lyapunov指数，并表明宇宙学常数会改变不稳定性时间尺度，而洛伦兹破缺参数则对光子球不稳定性产生非平凡的形变。我们的结果将零测地线识别为带电黑洞时空中洛伦兹破缺效应的敏感探针。
英文摘要：
We investigate null geodesics and their stability in four-dimensional charged Kalb-Ramond black holes with a cosmological constant. The non-vanishing vacuum expectation value of the background antisymmetric tensor field induces spontaneous Lorentz symmetry breaking, controlled by a dimensionless parameter $l$, and deforms the Reissner-Nordström-(A)dS geometry. We derive the effective potential for massless particles and obtain analytic expressions for the photon-sphere radius, critical impact parameter, capture cross section, and deflection trajectories. The limiting cases $l\rightarrow0$ recover the RN, RN-dS and RN-AdS geodesic structures, while finite values of $l$ shift the turning points, modify the bending of light and deform both first-kind and second-kind photon trajectories. In the AdS branch, we find a special limiting limaçon-type null geodesic whose angular structure is modified by the Kalb-Ramond parameter. We also compute the Lyapunov exponent of the unstable circular null orbit and show that the cosmological constant changes the instability timescale, whereas the Lorentz-violating parameter produces a non-trivial deformation of the photon-sphere instability. Our results identify null geodesics as sensitive probes of Lorentz-violating effects in charged black hole spacetimes.
