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

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 z ∈ R ⁴ the bilinear form g(z)[.,.] possesses one positive and three negative eigenvalues. The “pseudo-metric” induced by g is called Lorentz-metric.

Sponsored by M.P.I (fondi 60% “Problemi differenziali nonlineari e teoria dei punti critici; fondi 40% “Equazioni differenziali e calcolo delle variazioni”).