Constant-$r$ geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime

Understand

Herein we explore the non-equatorial constant-$r$ ("quasi-circular") geodesics (both timelike and null) in the Painleve-Gullstrand variant of the Lense-Thirring spacetime recently introduced by the current authors.

• Even though the spacetime is not spherically symmetric, shells of constant-$r$ geodesics still exist.
• Whereas the radial motion is (by construction) utterly trivial, determining the allowed locations of these constant-$r$ geodesics is decidedly non-trivial, and the stability analysis is equally tricky.
• Regarding the angular motion, these constant-$r$ orbits will be seen to exhibit both precession and nutation -- typically with incommensurate frequencies.