Related papers: Differential geometry, Palatini gravity and reduct…
An interpretation of Einstein-Hilbert gravity equations as Lagrangian reduction of Palatini gravity is made. The main technique involved in this task consists in representing the equations of motion as a set of differential forms on a…
The present article is devoted to the construction of a unified formalism for Palatini and unimodular gravity. The basic idea is to employ a relationship between unified formalism for a Griffiths variational problem and its classical…
A general $f(\mathcal{R})$ gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in…
We clarify the structure obtained in H\'elein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold. The obtained…
We consider a Palatini variation on a general $N$-Dimensional second order, torsion-free dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance…
A variational principle is suggested within Riemannnian geometry, in which an auxiliary metric and the Levi Civita connection are varied independently. The auxiliary metric plays the role of a Lagrange multiplier and introduces non-minimal…
Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini. The theory predicts the existence of a…
A variational principle was recently suggested by Goenner, where an independent metric generates the spacetime connection. It is pointed out here that the resulting theory is equivalent to the usual Palatini theory. However, a bimetric…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
A covariant Hamiltonian description of Palatini's gravity on manifolds with boundary is presented. Palatini's gravity appears as a gauge theory satisfying a constraint in a certain topological limit. This approach allows the consideration…
Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini…
Spacetime geometry is described by two -- {\em a priori} independent -- geometric structures: the symmetric connection $\Gamma$ and the metric tensor $g$. Metricity condition of $\Gamma$ (i.e. $\nabla g = 0$) is implied by the Palatini…
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…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
Recently a class of alternative theories of gravity which goes under the name f(R) gravity, has received considerable attention, mainly due to its interesting applications in cosmology. However, the phenomenology of such theories is not…
Inspired by problems arising in the geometrical treatment of Yang-Mills theories and Palatini's gravity, the covariant formulation of Hamiltonian dynamical systems as a Hamiltonian field theory of dimension $1+0$ on a manifold with boundary…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric…
In this paper, the hybrid metric-Palatini gravity is an approach to modified gravity in which is added to the usual Einstein-Hilbert action a supplementary term containing a Palatini-type correction of the form $f({\cal R},T)$. Here, ${\cal…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…