Massive particle surfaces and black hole shadows from intrinsic curvature

Abstract In a recent article Phys. Rev. D. 111 , 064001 (2025) a new geometric approach for studying massive particle surfaces was proposed. Using the Gaussian and geodesic curvatures defined over a two dimensional Riemannian metric, a criteria for the existence of massive particle surfaces was provided. In this work, we generalize these results by including stationary spacetime metrics. We surmount the difficulty of having a Jacobi metric of the Randers–Finsler type by using a 2-dimensional Riemannian metric that is obtained by a dimensional reduction of the spacetime metric along the admitted Killing vectors. We provide a condition for the existence of massive particle surfaces and a simple characterization for null and timelike trajectories only by using intrinsic curvatures of a 2-dimensional Riemannian surface. We study the massive particle surfaces of spacetimes that are not an asymptotically flat. We show that the Riemannian formalism can be used to study the shadows of the associated black holes. We show the existence of massive particle surfaces in the Kerr metric, the Kerr-(A)dS metric and in a solution, which is not asymptotically flat, of the Einsten–Maxwell-dilaton theory.