We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor Tμν(gαβ, ∂τgαβ, ∂τ∂σgαβ , . . . , ) constructed from sums of terms the involving contractions of the metric and powers of arbitrary covariant derivatives of th...

In this paper, we consider pseudosymmetric Lorentz Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of admits soliton have introduced according to the choice special tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again tensor, necessary conditions are given for form be sem...

We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form R2(1−α), with R the Ricci scalar and α a positive parameter smaller than one half, can generate sizable primordial tensor modes. We also suggest natural microscopic sources of these corrections and demonstrate that they generally lead to a nonzero and positive α. Furthermore we argue, that wit...

It is proved that the Riemann tensor squared is divergent as τ → 0 for a wide class of cosmological metrics with non-exceptional Kasner-like behaviour of scale factors as τ → 0, where τ is synchronous time. Using this result it is shown that non-trivial generalization of the spherically-symmetric Tangherlini solution to the case of n Ricci-flat internal spaces [13] has a divergent Riemann tenso...

Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and dimension of the group orbits as well as the Petrov type are constant, the aim of this work is to include the Segre types of the Ricci tensor (and hence of the Eins...

Locally, a screen integrable globally null manifold $M$ splits through Riemannian leaf $M'$ of its distribution and curve $\mathcal{C}$ tangent to radical distribution. The carries lot geometric information about and, in fact, forms basis for the study expanding non-expanding horizons black hole theory. In present paper, we introduce degenerate Ricci-type flow via intrinsic Ricci tensor $M$. Se...