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

Abstract

Recent observations of the orbits of star clusters around Sgr $$A^\star $$ A ⋆ , 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.

Spherical Particle Orbits around a Rotating Black Hole in Massive Gravity

“…Additionally, the reflection symmetry of the RdRGT black hole can be explored, which may provide insights into the existence of curved accretion disks [51]. Moreover, numerical analyses of the radii of planar orbits can be conducted for various axially symmetric spacetimes, serving as tests for the analytical solutions [52]. These methods can also be extended to investigate spherical particle orbits and accretion in stationary black holes with quintessential parameters or minimally coupled scalar fields [53,54].…”

Analysis of the Geodesic Motions of Massive Particles in Kerr–Sen–AdS4 Spacetime

“…Other works (see, for example, refs. [28,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]) also discussed the possible geodesic motions in various spacetimes.…”