Inextendibilty of the Maximal Global Hyperbolic Development in Electrogowdy spacetimes

M Gramegna,M Crosta,M.L Ruggiero,Ernesto Nungesser

doi:10.1051/epjconf/20135801004

Abstract

The problem of determinism in General Relativity appears even if one assumes that the spacetime is globally hyperbolic, i.e. that it contains a hypersurface that is intersected by any causal curve exactly once. The strong cosmic censorship hypothesis is essentially the hypothesis that General Relativity is a predictable theory and thus a crucial issue in Classical General Relativity. We sketch here the proof for the case of Electrogowdy spacetimes.

Highlights

The first time when in the literature a time machine was decribed, was in 1887 in the novel “El Anacronómete” written by the spaniard Enrique Gaspar [1]
From the singularity theorems of Hawking and Penrose [5],[6],[7] we know that singularities appear under general physically reasonable assumptions, but we do not know what happens in the singularities without a theory of quantum gravity
A conjecture to solve the question of predictability is the strong cosmic censorship hypothesis of Penrose [8]

Summary

Gowdy symmetry

Gowdy spacetimes are vacuum spacetimes which model closed universes filled with gravitational waves of two polarizations [10]-[11]. We refer to [12] for a detailed mathematical discussion These spacetimes are a good toy model for the understanding of inhomogeneous and anisotropic cosmological models. The transformation which simultaneously maps x to −x and y to −y is an isometry With this group action the possible spatial topologies are basically S 3, S 2 × S 1 and T 3 and in the following the spatial topology is assumed to be the three-dimensional torus. A metric with Gowdy symmetry is said to be polarized if the individual transformations mapping x to −x and y to −y are symmetries, which has the physical interpretation that the gravitational waves have only one polarization. We will assume that our spacetime has a polarized Gowdy-symmetry

Polarized Gowdy metric

Maxwell field and new variables

Basic equations for Einstein-Maxwell assuming polarized Gowdy symmetry

Central results