Electron. J. Diff. Eqns., Vol. 2006(2006), No. 114, pp. 1-9.

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

Valeria Luisi

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.

Show me the PDF file (223K), TEX file, and other files for this article.

Valeria Luisi
Dipartimento di Matematica
Università degli Studi di Bari
Via E. Orabona 4, 70125 Bari, Italy
email: vluisi@dm.uniba.it

Return to the EJDE web page