The antecedent of Einstein field equations with Euclidean signature is the complex elliptic Monge-Ampère equation, CMA2. For elliptic CMA2 solutions determine hyper-Kähler, self-dual and therefore Ricci-flat metrics with Euclidean signature. We shall consider a symmetry reduction of CMA2 to solutions that admit only a single Killing vector. Systematic studies of vacuum metrics with one Killing ...

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 prove the stability of de Sitter space-time as a solution to Einstein-Vlasov system with massless particles. The semi-global Minkowski is also addressed. proof relies on conformal techniques, namely Friedrich's Einstein field equations. exploit invariance Vlasov equation cotangent bundle and adapt Kato's local existence theorem for symmetric hyperbolic systems long enough time solutions evol...

For more than a decade, cold atoms represented weakly interacting systems. Laser cooling achieved temperatures typically around 100 μK in a classical gas, far away from quantum degeneracy. Evaporative cooling led to Bose-Einstein condensation at temperatures typically around 100 nK. Bose-Einstein condensates are weakly interacting many-body systems described by mean field physics through the Gr...

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...

Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation eq...

In this paper we use a similarity transformation connecting some families of Nonlinear Schrödinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrödinger equation. This transformation allows one to apply all known results for that equation to the original non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, us...

Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea contrasts with the recently proposed premetric electrodynamics by Hehl and Obukhov. In the teleparallel case the definition of the electric field is obtained stra...

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some...

where Lm is the matter part Lagrangian. The gravitational field equation is presented in Eq. (2) of [1]. In contrast with the situation with generalized f(φ,R) gravity in Eq. (27), the gravity with Ricci-curvature square term in the action does not have the conformal symmetry to Einstein gravity [2]. In [1] we analysed the gravitational wave and derived a fourth order differential equation. How...