$U(1)$ local strings in hybrid metric-Palatini gravity

TL;DR

This paper derives new stable cosmic string solutions within hybrid metric-Palatini gravity using a scalar-tensor approach, revealing how boundary conditions influence string parameters and expanding the understanding of such solutions in modified gravity theories.

Contribution

It introduces a method to find closed-form cosmic string solutions in hybrid metric-Palatini gravity, including cases with arbitrary potentials, and analyzes their stability and parameter dependence.

Findings

Derived a large class of new stable string solutions

Solutions depend on boundary values of scalar field and derivatives

Explored various potentials, including numerical and analytical cases

Abstract

In this work we made use of a general static cillindrically symmetric metric to find $U(1)$ local cosmic string solutions in the context of the hybrid metric-Palatini theory of gravity in it's scalar-tensor representation. After finding the dynamical equations for this particular case, we imposed boost invariance along $t$ and $z$ directions, which simplified the equations of motions, leaving only one single metric tensor component, $W^2(r)$. For an arbitrary potential $V(\phi)$, the solutions obtained can be put in a closed parametric form, with $\phi$ taken as a parameter. Several particular cases of the potential were studied, some yielding simple mathematical forms, others with only numerical solutions. With this approach, we obtain a large number of new stable stringlike solutions in hybrid metric-Palatini gravity, in which the parameters, like the scalar field, metric tensor components, and string tension, depend fundamentally on the boundary values of the scalar field, and its derivative, on the $r(0)$ circular axis.