We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold M admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics η on M × R such that (M × R, η) admit Einstein spinors (resp. weak Killing spinors). To prove the result we split the Einstein-Dirac equ...

We investigate the experimental limits of validity of the Stokes–Einstein equation. There is an important difference between diffusion and self-diffusion. The experimental evidences show, that in the case of selfdiffusion the product Dg/T is constant and the Stokes–Einstein equation is still valid. On the other hand, comparison of existing experimental data, on viscosity g and diffusion coeffic...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

In this paper we study pointwise projectively related Einstein metrics (having the same geodesics as point sets). We show that pointwise projectively related Einstein metrics satisfy a simple equation along geodesics. In particular, we show that if two pointwise projectively related Einstein metrics are complete with negative Einstein constants , then one is a multiple of another.

We show that Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength, mean field limit. Unlike nonlinear Dirac equations posited by particle theorists, which are designed to preserve the principle of relativity, i.e., Poincaré covariance, the nonlinear Dirac equation for Bose-Einstein condensates breaks this symmetry. We presen...

the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long time a mystery to be conquered. accordingly, the aim of this expository article is to present (i) the einstein relativistic vector addition, (ii) the resulting einstein scalar multiplication, (iii) the einstein rel...

The vacuum solution ds = dx + x dy + 2 dz dt + lnx dt of the Einstein gravitational field equation follows from the general ansatz ds = dx + gαβ(x) dx dx but fails to follow from it if the symmetric matrix gαβ(x) is assumed to be in diagonal form. KEY: Vacuum solution, Einstein field equation, symmetries, diagonalization

We prove that given a solution of the Einstein equations gab for the matter field Tab, an autoparallel null vector field l a and a solution (lalc, Tac) of the linearized Einstein equation on the given background, the Kerr-Schild metric gac + λlalc (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor Tac + λTac + λl(aTc)bl . The mixed form of the Ei...

the only justification for the einstein velocity addition law appeared to be its empirical adequacy, so that the intrinsic beauty and harmony in einstein addition remained for a long timea mystery to be conquered. accordingly, the aim of this expository article is to present(i) the einstein relativistic vector addition,(ii) the resulting einstein scalar multiplication,(iii) the einstein relativ...