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...

In the present paper, we have studied M -projectively flat generalized Sasakian space form, η-Einstein generalized Sasakian space form and irrotational M -projective curvature tensor on a Sasakian space form.

We use the recent discovered x−ψ duality to parameterize spacetime in terms of wave functions and quantum prepotentials. The components of metric, connection, curvature, Ricci tensor and scalar curvature as well as Einstein equations in this parameterization are

Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.

We characterize the Einstein tensor as the only, up to a constant factor, 2covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and invariant under constant rescalings of the metric. Since these two conditions are also satisfied by the energy-impulse tensor of a relativistic space-time, we discuss how this theorem and its variations can be used to derive ...

This paper attempts to define a generalisation of the standard Einstein condition (in conformal/metric geometry) to any parabolic geometry. To do so, it shows that any preserved involution σ of the adjoint bundle A gives rise, given certain algebraic conditions, to a unique preferred affine connection ∇ with covariantly constant rho-tensor P, compatible with the algebraic bracket on A. These co...

Given a convex body K ⊂ Rn with the barycenter at the origin we consider the corresponding Kähler-Einstein equation e = detDΦ. If K is a simplex, then the Ricci tensor of the Hessian metric DΦ is constant and equals n−1 4(n+1) . We conjecture that the Ricci tensor of D Φ for arbitrary K is uniformly bounded by n−1 4(n+1) and verify this conjecture in the two-dimensional case. The general case r...

In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the Einstein frame is used and the dynamics of general relativity with a minimally coupled scalar field are derived for a generic potential. It is shown that the dyna...

We give a detailed study of the critical points of the potentials of the simplest non-trivial N = 2 gauged Yang-Mills/Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is SO(1, 1)×SO(2, 1)/SO(2). The possible gauge groups are SO(2)×U(1)R and SO(1, 1) × U(1)R, where U(1)R is a subgroup of the R-symmetry group SU(2)R, and SO(2) and SO(1, 1) are...