Schwarzschild电磁黑洞的测地线结构
The geodesics structure of Schwarzschild electromagnetic black hole
摘要：
研究了均匀电磁场中静止质量的测地线方程。由于电磁场的作用，地平线收缩，测地线被修正。通过分析无质量粒子和有质量粒子的有效势的行为，我们研究了径向和圆形轨迹。精确求解了光子和粒子的径向测地线。结果表明，粒子在有限的固有时间内落向视界，速度减慢，到达奇点的时间比Schwarzschild情形长。研究了类时圆测地线和零圆测地线。证明了光子不存在稳定的圆轨道，而有质量粒子存在稳定和不稳定的第二类轨道。得到了最内层圆轨道的精确解析解。结果表明，由于电磁场的存在，ISCO的半径缩小。
英文摘要：
The geodesic equations are considered in static mass imbedded in a uniform electromagnetic field. Due to electromagnetic field horizon shrinks and geodesics are modified. By analyzing the behavior of the effective potentials for the massless and massive particle we study the radial and circular trajectories. Radial geodesics for both photons and particles are solved exactly. It is shown that a particle falls toward the horizon in a finite proper time slows down so that the particle reaches the singularity in longer time than Schwarzschild case. Timelike and null circular geodesics are investigated. We have shown that, there is no stable circular orbits for photons, however stable and unstable second kind orbits are exists for massive particle. An exact analytical solution for the innermost circular orbits (ISCO) has been obtained. It has been shown that the radius of ISCO shrinks due to the presence of electromagnetic field.
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