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 ...

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...

The asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) metric defines invariants of the AHE metric and of a metric in the induced conformal class at infinity. These have been of recent interest, motivated in part by the AdS/CFT correspondence in physics. In this paper we derive some new properties of these invariants. Let (X, g+) be AHE with smooth conformal infin...

‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.

We demonstrate the existence of phase fluctuations in elongated Bose-Einstein Condensates (BECs) and study the dependence of those fluctuations on the system parameters. A strong dependence on temperature , atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase coherence length is s...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.