Periodic Trajectories for the Lorentz-Metric of a Static Gravitational Field

  • Vieri Benci
  • Donato Fortunato
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 4)

Abstract

In General Relativity a gravitational field is described by a symmetric, second order tensor
$$ g \equiv g(z)\left[ {.,.} \right]z = ({z_0},...,{z_3})\varepsilon {^4} $$
on the space-time manifold R 4The tensor g is assumed to have the signature +, −, −, −; namely for all zR 4 the bilinear form g(z)[.,.] possesses one positive and three negative eigenvalues. The “pseudo-metric” induced by g is called Lorentz-metric.

Keywords

Manifold 

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Vieri Benci
    • 1
  • Donato Fortunato
    • 2
  1. 1.Istituto di MatematicheApplicate — UniversitàPisaItaly
  2. 2.Dipartimento di MatematicaUniversitàBariItaly

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