In this paper we examine homogeneous Einstein–Weyl structures and classify them on compact irreducible symmetric spaces. We find that the invariant Einstein–Weyl equation is very restrictive: Einstein–Weyl structures occur only on those spaces for which the isotropy representation has a trivial component, for example, the total space of a circle bundle.

In this paper, we consider Einstein–Hilbert gravity in the presence of cosmological constant with cylindrical symmetry to introduce black hole solution model. Here, solve Einstein’s vacuum field equation, and then calculate appropriate metric for problem.

An isotropic electromagnetic field in a plasma of thermalized electrons undergoes changes energy as result Compton scattering and an Einstein–Hopf drag force on the electrons, eventually approaching Bose–Einstein photon distribution at electron temperature. The rate change due to combined effects is shown be described by Kompaneets equation for diffusion frequency space. A similarity noted betw...

We report a numerical study of turbulence and Bose-Einstein condensation within the two-dimmensional GrossPitaevski model with repulsive interaction. In presence of weak forcing localized around some wave number in the Fourier space, we observe three qualitatively different evolution stages. At the initial stage a thermodynamic energy equipartition spectrum forms at both smaller and larger scal...

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.

We analyse prospects for the use of Bose–Einstein condensates as condensedmatter systems suitable for generating a generic ‘effective metric’, and for mimicking kinematic aspects of general relativity. We extend the analysis due to Garay et al (2000 Phys. Rev. Lett. 85 4643, 2001 Phys. Rev. A 63 023611). Taking a long-term view, we ask what the ultimate limits of such a system might be. To this...

We propose a criterion for the validity of semiclassical gravity ~SCG! which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equatio...

A system of effective Einstein equations for spatially averaged scalar variables of inhomogeneous cosmological models can be solved by providing a ‘cosmic equation of state’. Recent efforts to explain Dark Energy focus on ‘backreaction effects’ of inhomogeneities on the effective evolution of cosmological parameters in our Hubble volume, avoiding a cosmological constant in the equation of state...