Related papers: Nonlocal gravity: Conformally flat spacetimes
First and foremost, we show that a 4-dimensional conformally flat generalized Ricci recurrent spacetime $(GR)_4$ is an Einstein manifold. We examine such a spacetime as a solution of $f(R, G)$-gravity theory and it is shown that the…
We hereby study the properties of a large class of weakly nonlocal gravitational theories around the (anti-) de Sitter spacetime background. In particular, we explicitly prove that the kinetic operator for the graviton field has the same…
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
The gravitation field of the flat plate was investigated. It have been shown that there exist the internal solution of Einstein equations sewed together with external one, which described a ''homogeneous'' gravitational field.
A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
We propose a formulation of gravity theory in the form of a field theory in a flat space-time with a number of dimensions greater than four. Configurations of the field under consideration describe the splitting of this space-time into a…
Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their…
Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static…
In this article, it is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of de Sitter-like spacetimes with spatial sections…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
We consider the G\"odel universe within the context of the local limit of nonlocal gravity. This theory differs from Einstein's general relativity (GR) through the existence of a scalar susceptibility function $S(x)$ that is a…
We consider conformal and scale-invariant gravities in d dimensions, with a special focus on pure $R^2$ gravity in the scale-invariant case. In four dimensions, the structure of these theories is well known. However, in dimensions larger…