Stationary cylindrically symmetric spacetimes with a massless scalar field and a non-positive cosmological constant

TL;DR

This paper derives the most general stationary cylindrically symmetric solutions of Einstein's equations coupled with a massless scalar field and a non-positive cosmological constant, revealing new algebraic types and topological features.

Contribution

It provides the complete family of solutions characterized by four constants, including new type O and D spacetimes influenced by scalar fields and topology.

Findings

Solutions include type I, O, and D spacetimes.

Scalar field affects algebraic classification.

Curvature singularities can be removed with phantom scalar fields.

Abstract

The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants. Two of these essential parameters have a local meaning and characterize the gravitational field strength. The other two have a topological origin, as they define an improper coordinate transformation that provides the stationary solution from the static one. The Petrov scheme is considered to explore the effects of the scalar field on the algebraic classification of the solutions. In general, these spacetimes are of type I. However, the presence of the scalar field allows us to find a non-vacuum type O solution and a wider family of type D spacetimes, in comparison with the vacuum case. The mass and angular momentum of the solution are computed using the Regge-Teitelboim method in the case of a negative cosmological constant. In absence of a cosmological constant, the curvature singularities in the vacuum solutions can be removed by including a phantom scalar field, yielding non-trivial locally homogeneous spacetimes. These spacetimes are of particular interest, as they have all their curvature invariants constant.