This paper is aimed to elaborate the problem of energy-momentum in General Relativity. In this connection, we use the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Möller to compute the energy-momentum densities for two exact solutions of Einstein field equations. The spacetimes under consideration are the non-null EinsteinMaxwell solutions and the singularity-free cosmological mod...

In this article, we examine the possibility that there exist special scalar-tensor theories of gravity with completely nonsingular FRW solutions. Our investigation in fact shows that while most probes living in such a Universe never see the singularity, gravity waves always do. This is because they couple to both the metric and the scalar field, in a way which effectively forces them to move al...

The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an ε-anti-Kähler manifold. Firstly, we deduce relation between Riemannian connection connections. Then, present some results concerning torsion tensors these In addition, find curvature tensor, Ricci tensor scalar such search conditions for manifold to be Einstein space with respect Finally,...

A historical account of Einstein’s Fernparallelismus approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a spacetime characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appe...

The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, D̂[g] (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metri...

We construct a 2-parameter family FZ of Riemannian metrics on the twistor space Z of a positive quaternion Kähler manifold M satisfying the following properties : (1) the family FZ contains an Einstein metric gZ and its scalings, (2) the family FZ is closed under the operation of making the convex sums, (3) the Ricci map g 7→ Ric(g) defines a dynamical system on the family FZ, (4) the Ricci flo...

The ultrashort unitary (4,0) supermultiplet of 6d superconformal algebra OSp(8*|8) reduces to the CPT-self conjugate 4d SU(2,2|8) that represents fields maximal N=8 supergravity. graviton in multiplet is described by a mixed tensor gauge field which can not be identified with standard metric 6d. Furthermore obtained as double copy (2,0) conformal whose interacting theories are non-Lagrangian. I...

We extend Maldacena's argument, namely, obtaining Einstein gravity from Conformal Gravity, to six dimensional manifolds. The proof relies on a particular combination of conformal (and topological) invariants, which makes manifest the fact that 6D Gravity admits an sector. Then, by taking generalized Neumann boundary conditions, action reduces renormalized Einstein-AdS action. These restrictions...