Hybrid metric-Palatini gravity: Regular stringlike configurations

TL;DR

This paper explores regular, stringlike vacuum solutions in hybrid metric-Palatini gravity, revealing their properties and establishing a correspondence between Einstein and Jordan frames, with implications for scalar-tensor and $f(R)$ theories.

Contribution

It introduces a method to construct stringlike solutions in hybrid metric-Palatini gravity and demonstrates their properties and frame correspondence.

Findings

Existence of regular stringlike solutions with Minkowski far from the axis

A one-to-one correspondence between Einstein and Jordan frame solutions

An algorithm for constructing solutions in scalar-tensor theories

Abstract

We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and to produce a certain progress in cosmology. We use HMPG in its well-known scalar-tensor representation. The latter coincides with general relativity containing, as a source of gravity, a conformally coupled scalar field $\phi$ and a self-interaction potential $V(\phi)$. The $\phi$ field can be canonical or phantom, and accordingly the theory splits into canonical and phantom sectors. We seek solitonic (stringlike) vacuum solutions of HMPG, that is, completely regular solutions with Minkowski metric far from the symmetry axis, with a possible angular deficit. A transition of the theory to the Einstein conformal frame is used as a tool, and many of the results apply to the general Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories as well as $f(R)$ theories of gravity. One of these results is a one-to-one correspondence between stringlike solutions in the Einstein and Jordan frames if the conformal factor that connects them is everywhere regular. An algorithm for construction of stringlike solutions in HMPG and scalar-tensor theories is suggested, and some examples of such solutions are obtained and discussed.