All analytic solutions for geodesic motion in axially symmetric space-times

Abstract

Recent observations of the orbits of star clusters around Sgr $A^{\star }$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up with a method to provide all the possible geodesics in an axially symmetric space-time. The Kerr metric is explicitly worked out, recovering the Schwarzschild geodesics in the static limit. We also found the most general Killing tensor and its associated constant of motion for an axisymmetric space-time. The relevance of these results is crucial to understanding the different scenarios and the fundamental nature of the compact object at the galactic center.

References in corpus (4)

• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Gravitational Test Beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole
• Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals
• Kerr-Newman black hole lensing of relativistic massive particles in the weak field limit