Bose-Einstein condensate strings

TL;DR

This paper explores the theoretical existence of gravitationally bound Bose-Einstein condensate strings in general relativity, analyzing their properties and stability through numerical solutions of the field equations.

Contribution

It introduces a model of BEC strings considering both interaction and quantum pressures, providing new insights into their structure and stability in astrophysical contexts.

Findings

Identified stable BEC string configurations with specific mass densities and radii.

Showed the dependence of string properties on particle mass and scattering length.

Demonstrated the significance of quantum pressure in certain regimes.

Abstract

We consider the possible existence of gravitationally bound general relativistic strings consisting of Bose-Einstein condensate (BEC) matter which is described, in the Newtonian limit, by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive interparticle interactions. In the Madelung representation of the wave function, the quantum dynamics of the condensate can be formulated in terms of the classical continuity equation and the hydrodynamic Euler equations. In the case of a condensate with quartic nonlinearity, the condensates can be described as a gas with two pressure terms, the interaction pressure, which is proportional to the square of the matter density, and the quantum pressure, which is without any classical analogue though, when the number of particles in the system is high enough, the latter may be neglected. Assuming cylindrical symmetry, we analyze the physical properties of the BEC strings in both the interaction pressure and quantum pressure dominated limits, by numerically integrating the gravitational field equations. In this way we obtain a large class of stable stringlike astrophysical objects, whose basic parameters (mass density and radius) depend sensitively on the mass and scattering length of the condensate particle, as well as on the quantum pressure of the Bose-Einstein gas.