Proca Q Tubes and their Coupling to Gravity

TL;DR

This paper investigates Proca-Q-tubes, cylindrical solutions of a complex vector field coupled to gravity, analyzing their properties, existence conditions, and behavior both with and without gravitational effects.

Contribution

It introduces and characterizes Proca-Q-tubes, extending spherical Proca-Q-balls to cylindrical symmetry and exploring their properties in the presence and absence of gravity.

Findings

Existence of regular Proca-Q-tube solutions with finite mass and charge.

Detailed analysis of the parameter space for solution existence.

Construction of gravitating Proca-Q-tubes and their properties.

Abstract

The Einstein-Proca system is studied in the case of a complex vector-field self-interacting through an appropriate potential with a global U(1) symmetry. The corresponding equations for a static, cylindrically symmetric metric and matter fields are then constructed and solved. In the probe limit (no gravity), it is shown that the equations admit at least two classes of regular solutions distinguished by the asymptotic behavior of the matter fields. One of these classes corresponds to lumps of vector fields localized in a cylindrical region, we naturally call these solutions "Proca-Q-tubes". They constitute the cylindrical counterparts of spherical Proca-Q-balls constructed recently, they can be characterized by finite mass and charge per unit-length of the tube. The domain of existence of these Proca-Q-tubes with respect to the coupling constants determining the potential is studied in detail. Finally, the gravitating Proca-Q-tubes are constructed and studied.