Related papers: Palatini's cousin: A New Variational Principle
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
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…
It has been suggested that the recent acceleration of the expansion of the Universe is due a modified gravitational action consisting of the Einstein-Hilbert term plus a term proportional to the reciprocal of the Ricci scalar. Although the…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
We study nonlinear gravity theories in both the metric and the Palatini (metric-affine) formalisms. The nonlinear character of the gravity lagrangian in the metric formalism causes the appearance of a scalar source of matter in Einstein's…
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…
In this paper a hidden extra symmetry of conformally invariant Lagrangians occuring in physics is pointed out. This symmetry is most apparent in a metric independent, i.e. in a Palatini-like presentation of the variational problem. In such…
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 Euler-Lagrange equations for some class of gravitational actions are calculated by means of Palatini principle. Polynomial structures with Einstein metrics appear among extremals of this variational problem.
In the Palatini action of general relativity the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the…
I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the…
We extend the parametric geometry of numbers (initiated by Schmidt and Summerer, and deepened by Roy) to Diophantine approximation for systems of $m$ linear forms in $n$ variables, and establish a new connection to the metric theory via a…
We present the first formulation of the recently proposed $f(R,\mathcal{L}_m,T)$ theory of gravity within the Palatini formalism, a well-known alternative variational approach where the metric and connection are treated as independent…
The way one chooses to couple gravity to matter is an essential characteristic of any gravitational theory. In theories where the gravitational field is allowed to have more degrees of freedom than those of General Relativity (e.g.…
Corrections to Einstein's equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast to the…
Laws of motion given in terms of differential equations can not always be derived from an action principle, at least not without introducing auxiliary variables. By allowing auxiliary variables, e.g. in the form of Lagrange multipliers, an…
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…
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these…
We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that in…
We study models where a scalar field has derivative and non-derivative couplings to the Ricci tensor and the co-Ricci tensor with a view to inflation. We consider both the metric formulation and the Palatini formulation. In the Palatini…