A spacetime with closed timelike geodesics everywhere

TL;DR

This paper introduces a new class of Einstein field solutions describing stationary, cylindrically symmetric spacetimes with pervasive closed timelike geodesics, involving magnetic fields, perfect fluids, and negative cosmological constants.

Contribution

It presents novel solutions to Einstein's equations featuring closed timelike geodesics throughout the spacetime, expanding understanding of possible spacetime geometries.

Findings

Spacetimes with closed timelike geodesics everywhere outside the axis.

Inclusion of magnetic fields and perfect fluids in these solutions.

Existence of Lorentz invariant vacuum with negative cosmological constant.

Abstract

In the present article we find a new class of solutions of Einstein's field equations. It describes stationary, cylindrically symmetric spacetimes with closed timelike geodesics everywhere outside the symmetry axis. These spacetimes contain a magnetic field parallel to the axis, a perfect fluid with constant density and pressure, and Lorentz invariant vacuum with energy density represented by a negative cosmological constant.