Bose-Einstein condensation is the occupation of a single quantum state by a large number of identical particles. This implies that particles are assumed to be bosons, satisfying the Bose-Einstein statistics allowing for many particles to pile up in the same quantum state. This is contrary to fermions, satisfying the Fermi-Dirac statistics, for which the Pauli exclusion principle does not allow ...

We classify solvable Lie groups with free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six others: (here f(...

Riemannian Killing conserved currents are used to find the energy spectra of classical spinning particles moving around a spinning string in Einstein-Cartan (EC) theory of gravity. It is shown that a continuos spectrum is obtained for planar open orbits and the energy shift of spectrum is obtained for circular planar orbits. A spin-spin effect between the spin of the test particle and the spin ...

A conformal Lie group is a manifold $(M,c)$ such that $M$ has structure and $c$ the defined by left-invariant metric $g$ on $M$. We study Weyl-Einstein structures solvable groups their compact quotients. In case, we show every solvmanifold carrying Einstein. also there are no non-abelian nilpotent groups, classify them in almost abelian case. Furthermore, determine precise list (up to automorph...

An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable ...

Density linear perturbations in Einstein-Cartan two fluid cosmolo-gies where the outer model is an isotropic Friedmann solution with closed model while the inner model is a flat anisotropic Einstein-Cartan (EC) cosmology with shear are computed by taking into consideration superhorizon situations.This situation is in agreement with the present isotropy of the Cosmic Background Radiation where t...

In this work, we give a general class of solutions of the spinning cosmic string in Einstein’s theory of gravity. After treating same problem in Einstein Cartan (EC) theory of gravity, the exact solution satisfying both exterior and interior space-times representing a spin fluid moving along the symmetry axis is presented in the EC theory. The existence of closed timelike curves in this spaceti...