We show that as in the case of isotropic models, `Dirac Algorithm' and `Modified Horowitz' Formalism' lead to identical phase-space structure Hamiltonian for gravitational action with curvature squared terms, anisotropic space-time, viz, Bianchi-I, Bianchi-III Kantowski-Sachs models too.

For general relativistic spacetimes filled with irrotational ‘dust’ a generalized form of Friedmann’s equations for an ‘effective’ expansion factor aD(t) of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous–isotropic cosmologies, the new equations include the ‘backreaction effect’ of inhomogeneities on the average expansion of the mod...

We show that a closed four-manifold with \(4\frac{1}{2}\)-positive curvature operator of the second kind is diffeomorphic to spherical space form. The assumption sharp as both \({\mathbb{CP}\mathbb{}}^2\) and \({\mathbb {S}}^3 \times {\mathbb {S}}^1\) have \(4\frac{1}{2}\)-nonnegative kind. In higher dimensions \(n\ge 5\), we Riemannian manifolds are homeomorphic forms. These results proved by ...

The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M,L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (L̃(x, y) = L(x, y) + B(x, y)with B := g(ζ, η); ζ bei...

The destructive interference of the neighbouring field configurations with infinite classical action in gravitational path integral approach serves as a dynamical mechanism resolving black hole singularity problem. It also provides an isotropic and homogeneous early universe without need inflation. In this work, we elaborate on finite framework Horava-Lifshitz gravity -- ghost-free QFT. Assumin...

We study the existence of a natural ‘linearisation’ process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new insights are being obtained in the fine structure of affine bundles over an anc...

The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M,L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (L̃(x, y) = L(x, y) + B(x, y)with B := g(ζ, η); ζ bei...