Related papers: On generalized quasi-Einstein GRW space-times
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
The question of existence of general, asymptotically flat radiative spacetimes and examples of explicit classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. The examples are…
We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced…
We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence condition.
A rigidly rotating incompressible perfect fluid solution of Einstein's gravitational equations is discussed. The Petrov type is D, and the metric admits a four-parameter isometry group. The Gaussian curvature of the constant-pressure…
We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a…
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite…
We analyze a proper time renormalization group equation for Quantum Einstein Gravity in the Einstein-Hilbert truncation and compare its predictions to those of the conceptually different exact renormalization group equation of the effective…
In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold…
We establish a lower bound on the total mass of the time slices of (n + 1)-dimensional asymptotically flat standard static spacetimes under the timelike convergence condition. The inequality can be viewed equivalently as a Minkowski-type…
The prime object of this article is to study the perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity, when $\eta$-Ricci solitons, gradient $\eta$-Ricci solitons, gradient Einstein Solitons and gradient $m$-quasi Einstein solitons are…
In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…
Strictly respecting the Einstein equations and supposing space-time is a medium, we derive the deformation of this medium by gravity. We derive the deformation in case of infinite plane, Robertson-Walker manifold, Schwarzschild manifold and…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
A new class of exact solutions of Einstein's field equations with a perfect fluid source, variable gravitational coupling $G$ and cosmological term $\Lambda$ for FRW spacetime is obtained by considering variable deceleration parameter…
When solving the equations of General Relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress-energy. This implies that for static and isotropic spacetimes, the most general natural…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient…
We investigate the geometrical and physical structures of a pseudo-symmetric spacetime $(PS)_4$ with timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed…
In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar…