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

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.

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

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