Null geodesics in the static black bottle spacetime

Abstract

This research analyses the spacetime geometry of the static black bottle by studying the geodesic motion of photons. Geodesic equations are found using the Hamilton–Jacobi formalism. The geodesics are then classified based on a set of appropriate conserved physical quantities. Effective potentials are used to visualise the allowed orbits. The classifications also vary based on the acceleration parameter of the spacetime. Analytical solutions are found using the Jacobi elliptic functions of the first and second kinds, \({{\,\textrm{sn}\,}}(u,m), {{\,\textrm{cn}\,}}(u,m)\). The geodesics are then visualised using isometric embedding alongside the horizons of the black bottle.