Closed orbits in axial symmetric Finslerian extension of a Schwarzschild black hole

The axial symmetric Finslerian extension of a Schwarzschild spacetime is a generalization of Schwarzschild spacetime. It will return to Schwarzschild spacetime while the Finslerian parameter epsilon 1/4 0. Closed orbits are an important geometrical subject in mathematics that will help us to understand the physical properties of black holes in a strong gravitational region. The closed orbits of the axial symmetric Finslerian extension of a Schwarzschild black hole have been investigated in this paper. We have found that one necessary condition for the orbits of a Finslerian black hole to be closed is that the Finslerian parameter epsilon be rational. The numerical results of closed orbits of a Finslerian black hole are shown. They confirm our conclusion of the existence conditions of closed orbits.

Automated summary

This paper investigates the closed orbits of the axial symmetric Finslerian extension of a Schwarzschild black hole and finds that a rational Finslerian parameter is necessary for closed orbits.