Light rays in static spacetimes with critical asymptotic behavior: A variational approach

Abstract

Let M = M0 x ℝ be a Lorentzian manifold equipped with the static metric ⟨•, •⟩z = ⟨•, •⟩ - β(x)dt2. The aim of this paper is investigating the existence of lightlike geodesics joining a point z0 = x0, t0 to a line γ = {x1} x ℝ when coefficient β has a quadratic asymptotic behavior by means of a variational approach.