The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detail how the gravitational anomalies originate from the modified Einstein equati...

The twistor space Z of self-dual positive Einstein manifolds naturally admits two 1-parameter families of Riemannian metrics, one is the family of canonical deformation metrics and the other is the family introduced by B. Chow and D. Yang in [C-Y]. The purpose of this paper is to compare these two families. In particular we compare the Ricci tensor and the behavior under the Ricci flow of these...

Why are there no fundamental scalar fields actually observed in physics today? Scalars are the simplest fields, but once we go beyond Galilean-Newtonian physics they appear only in speculations, as possible determinants of the gravitational constants in the so-called Scalar-Tensor theories in non-quantum physics, and as Higgs particles, dilatons, etc., in quantum physics. Actually, scalar field...

A multidimensional gravitational model on the manifold M = M0 × ∏ n i=1 Mi , where Mi are Einstein spaces (i ≥ 1), is studied. For N0 = dimM0 > 2 the σ model representation is considered and it is shown that the corresponding Euclidean Toda-like system does not satisfy the Adler-van-Moerbeke criterion. For M0 = R N0 , N0 = 3, 4, 6 (and the total dimension D = dimM = 11, 10, 11, respectively) no...

Solitons in the extended hydrodynamic model of dipolar Bose-Einstein condensate with quantum fluctuations are considered. This includes continuity equation for scalar field concentration, Euler vector velocity, pressure evolution second rank tensor pressure, and third tensor. Large amplitude soliton solution caused by part is found. It appears as bright soliton. Hence, it area compression numbe...

where Rij is the Ricci curvature tensor of the metric and R is its scalar curvature. This equation tells us how the metric tensor gij (i.e. the field mediating the gravitation) is obeying to constraints imposed by the energy-momentum tensor Tij , which encodes informations about the distribution of energy and momentum in spacetime. For simplicity we will assume in the following that Tij = 0, i....

It is proved that a compact Kähler manifold whose Ricci tensor has two distinct constant non-negative eigenvalues is locally the product of two Kähler-Einstein manifolds. A stronger result is established for the case of Kähler surfaces. Irreducible Kähler manifolds with two distinct constant eigenvalues of the Ricci tensor are shown to exist in various situations: there are homogeneous examples...

In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other ph...

The possibility of the cosmic string creation by the vacuum fluctuations of quantum fields in the self-consistent semiclassical theory of gravity is discussed. We use the approximate method for obtaining vacuum expectation value of the renormalized stress-energy tensor of conformally invariant quantum fields in static cylindrically symmetric spacetimes. We have obtained the particular solutions...


 This short paper compares the classical Newton gravitational equation to Einstein curvature tensor and shows that two are intimately related. The calculation expands force be more in line with Schwarzschild tensors.