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.