Métrica de Gödel

Abstract

The Gödel scenario is a static and spatially homogeneous geometric structure of the universe – but not acceptable as it is absent from Hubble expansion – generated by the symmetrical and uniform rotation of dust-like source matter (moment density, p ≥ 0), free from any interaction around a inertial axis according to the expectations of Modern Cosmology. The world lines of matter will all be parallel and equidistant. The Kantian concept of time is supported here, that is, there is no temporal structure that can be determined by the relativization of the main world lines. The possibility of traveling to the past from the future is brought about in this context through the families of causal geodesics with the same absolute time axis, or time-type closed curves (the so-called CTC’s, which comes from the acronym in english) with the same twist. Any event can contain a causal geodesic, discarding any singularity. In this work, this metric region of the curved spacetime will be developed, either with the original metric or with the adapted metric, according to the nature of the problems investigated. For example, the Klein-Gordon equation will require a parameterization class of the Gödel metric. These solutions of Einstein’s field equations ( ≠ 0) have greatly intrigued Theoretical Physics, especially Quantum Gravity and General Relativity itself. Therefore, some gravitational backgrounds have been chosen here to illustrate this.