Related papers: Palatini Variational Principle for an Extended Ein…
From the freedom exhibited by the generalized Einstein action proposed in [1], we show that we can construct the standard effective Einstein-Cartan action coupled to the fermionic matter without the usual current-current interaction and…
A novel Dirac Hamiltonian formulation of the first order Einstein-Hilbert (EH) action, in which algebraic constraints are not solved to eliminate fields from the action at the Lagrangian level, has been shown to lead to an action and a…
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…
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…
The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for…
An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the…
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel…
In the framework of the Einstein-Palatini formalism, even though the projective transformation connecting the arbitrary connection with the Levi Civita connection has been floating in the literature for a long time and perhaps the result…
By using the Hamilton-Jacobi [HJ] framework the three dimensional Palatini theory plus a Chern-Simons term [PCS] is analyzed. We report the complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential from which all symmetries of…
A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincare` group of the…
A canonical analysis of the Einstein-Hilbert action S_d (d>2) is considered, using the first order form with the metric and affine connection as independent fields. We adopt a conservative approach to using the Dirac constraint formalism;…
The Hamiltonian analysis for the Einstein's action in $ G\to 0 $ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $ Gto 0 $ for Einstein's action is devoid…
This article describes a formula for second variation of generalized Einstein-Hilbert functional on Riemannian manifolds. This work extends the definition of stable Einstein manifolds, and we present some properties.
We propose a new discrete approximation to the Einstein equations, based on the Capovilla-Dell-Jacobson form of the action for the Ashtekar variables. This formulation is analogous to the Regge calculus in that the curvature has support on…
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…
We reformulate the Palatini action for general relativity (GR) in terms of moving frames that exhibit local Galilean covariance in a large speed of light expansion. For this, we express the action in terms of variables that are adapted to a…
The Einstein field equations can be derived in $n$ dimensions ($n>2$) by the variations of the Palatini action. The Killing reduction of 5-dimensional Palatini action is studied on the assumption that pentads and Lorentz connections are…
In this paper, we define the bimetric spectral Einstein-Hilbert action which generalizes the spectral Einstein-Hilbert action. We compute the bimetric spectral Einstein-Hilbert action for the Lorentz warped product. Thus, we get the…
It has been shown that the canonical structure of the first order Einstein-Hilbert (1EH) action involves three generations of constraints and that these can be used to find the generator of a gauge transformation which leaves the action…
We carry out the canonical analysis of the $n$-dimensional Palatini action with or without a cosmological constant $(n\geq3)$ introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing…