Geodesic
Light rays in static spacetimes with critical asymptotic behavior: a variational approach
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 53C50, 58E05, 58E10
Keywords: static spacetime, light ray, quadratic asymptotic behavior, Fermat principle, Ljusternik-schnirelman category 
@article{EJDE_2006__2006__a5,
     author = {Luisi,  Valeria},
     title = {Light rays in static spacetimes with critical asymptotic behavior: a variational approach},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1112.53055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a5/}
}
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%A Luisi,  Valeria
%T Light rays in static spacetimes with critical asymptotic behavior: a variational approach
%J Electronic journal of differential equations
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Luisi,  Valeria. Light rays in static spacetimes with critical asymptotic behavior: a variational approach. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a5/