Related papers: Modified Einstein equations
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the…
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein…
A mathematical complication due to an unnecessary formal assumption concerning the variational principle of general relativity theory, which apparently bothered Einstein and Hilbert, is shown and cleared up. Some historical confusion seems…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
The main goal of this paper is to get in a straightforward form the field equations in metric f(R) gravity, using elementary variational principles and adding a boundary term in the action, instead of the usual treatment in an equivalent…
The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the…
It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a…
Careful analysis of parametrized variational principles in mechanics and field theory leads to a generalization of Einstein theory that includes a cosmological stress tensor. This generalization also follows by restricting variations of the…
In this study, the effects of the generalized uncertainty principle on the theory of gravity are analyzed. Inspired by Verlinde's entropic gravity approach and using the modified Unruh temperature, the generalized Einstein field equations…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
The Einstein-Hilbert action for general relativity is not well posed in terms of the metric $g_{ab}$ as a dynamical variable. There have been many proposals to obtain an well posed action principle for general relativity, e.g., addition of…
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar…
We develop a novel approach to gravity in which gravity is described by a matrix-valued symmetric two-tensor field and construct an invariant functional that reduces to the standard Einstein-Hilbert action in the commutative limit. We also…
Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the…
We show that generalizations of general relativity theory, which consist in replacing the Hilbert Lagrangian $L_{Hilbert} = \frac 1{16\pi} \sqrt{|g|} R$ by a generic scalar density $L=L(g_{\mu\nu}, R^\lambda_{\mu\nu\kappa})$ depending upon…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…