JournalsaihpcVol. 7, No. 1pp. 27–35

Existence of geodesics for the Lorentz metric of a stationary gravitational field

  • Vieri Benci

    Istituto di Matematiche Applicate, Università, 56100 Pisa, Italy
  • Donato Fortunato

    Dipartimento di Matematica, Università, 70125 Bari, Italy
Existence of geodesics for the Lorentz metric of a stationary gravitational field  cover
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Abstract

Let g = g(z) (z = (z0, …, z3) ∈ ℝ4) be a Lorentz metric (with signature +, −, −, −) on the space-time manifold ℝ4. Suppose that g is stationary, i.e. g does not depend on z0. Then we prove, under some other mild assumptions on g, that for any two points a, b ∈ ℝ4 there exists a geodesic, with respect to g, joining a and b.

Résumé

Soit g = g(z) (z = (z0, …, z3) ∈ ℝ4) une métrique de Lorentz (avec signature +, −, −, −) sur l’espace-temps ℝ4. On suppose que g soit stationnaire, c’est-à-dire indépendante de z0. Nous démontrons, sous des autres convenable hypothèses sur g, l’existence d’arcs de géodésique joignant deux points a, b arbitrairement donné dans ℝ4.

Cite this article

Vieri Benci, Donato Fortunato, Existence of geodesics for the Lorentz metric of a stationary gravitational field . Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 1, pp. 27–35

DOI 10.1016/S0294-1449(16)30308-0