Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 114, pp. 1-9.

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

Author: Valeria Luisi (Univ. degli Studi di Bari, Italy)
	 
Abstract: 
 Let $\mathcal{M}=\mathcal{M}_{0}\times \mathbb{R}$ be a Lorentzian
 manifold equipped with the static metric
 $\langle \cdot ,\cdot \rangle _{z}=\langle \cdot ,\cdot \rangle
 -\beta (x)dt^{2}$.
 The aim of this paper is investigating the existence of lightlike
 geodesics joining a point $z_{0}=(x_{0},t_{0})$ to a line
 $\gamma =\{ x_{1}\} \times \mathbb{R}$ when coefficient
 $\beta $ has a quadratic asymptotic behavior by means of a variational
 approach.
 
Submitted November 28, 2005. Published September 21, 2006.
Math Subject Classifications: 53C50, 58E05, 58E10.
Key Words: Static spacetime; light ray; 
           quadratic asymptotic behavior; Fermat principle;
           Ljusternik-Schnirelman category.