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arXiv 1710.09581gr-qc
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球对称裸奇点的周期轨道

Periodic orbits around a spherically symmetric naked singularity

Gulmina Zaman Babar, Adil Zaman Babar, Yen-Kheng Lim

摘要:

利用测地线方程的哈密顿形式研究了Fisher/Janis-Newman-Winicour(F/JNW)时空中类时试验粒子的运动.时空的特征是它的质量参数$r_g$和标量场参数$ν$。计算了最内界和稳定圆轨道,分析了有效势。与早期文献中的数值结果一致,对于$ν<1/2$,具有非零角动量的粒子遇到无限大的势垒,阻止它们到达$r=r_g$的裸奇点。还得到了时空中的周期轨道。与Schwarzschild黑洞的周期轨道相比,在F/JNW时空中,相同的周期轨道所需要的能量要低得多.

英文摘要:

The motion of time-like test particles in the Fisher/Janis-Newman-Winicour (F/JNW) spacetime is studied with the Hamiltonian formulation of the geodesic equations. The spacetime is characterised by its mass parameter $r_g$ and scalar field parameter $ν$. The innermost bound and stable circular orbits are calculated and the effective potential is analysed. Consistent with numerical results in earlier literature, for $ν<1/2$, particles with non-zero angular momentum encounter an infinite potential barrier, preventing them from reaching the naked singularity at $r=r_g$. Periodic orbits in the spacetime are also obtained. Compared to the periodic orbits around the Schwarzschild black hole, it is found that typically lower energies are required for the same orbits in the F/JNW spacetime.

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