Two conserved angular momenta in schwarzschild spacetime geodesics

Abstract

The present study investigated the geodesic paths in the 3+1 dimensional Schwarzschild spacetime. Four conserved parameters were found: The first is the conserved total energy: The second is the coordinate-invariant metrics: And the final two are the angular momenta (Pθ and P ) in the spherical coordinate. For θ = π/2 and when excluding a 1/c 2 term in the equation of motion, we recover the orbit equation of the two-body problem. But when not excluding that term, we recover the orbit precession, e.g. the perihelion precession of Mercury. When the value θ is not fixed, we found the equation of motion to be the radius r(θ) as a function of θ, which is similar to the function for a fixed value of θ. © Published under licence by IOP Publishing Ltd.