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It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in usual way is automatically diffeomorphism…

It is possible to provide a thermodynamic interpretation for the field equations in any diffeomorphism invariant theory of gravity. This insight, in turn, leads us to the possibility of deriving the gravitational field equations from…

The notion of diffeomorphism invariance and general covariance are conceptually delicate issues for the field equations and the actions. A thorough study on the original Einstein field equation and its two modifications by Einstein is…

This short note is devoted to the Hamiltonian analysis of three dimensional gravity action that was proposed recently in [arXiv:1309.7231]. We modify given action in order to be invariant under non-relativistic diffeomorphism. Then we…

A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…

Motivated by the analogy between the spacetime and the solid with inhomogeneous elasticity modulus, we present an alternative method to obtain the field equation of any diffeomorphism-invariant gravity, by extremizing the constructed…

We study certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, we consider specific examples of invariant actions, extended gauge symmetry as well as an application to the theory of…

We present a method of constructing perturbative equations of motion for the geometric background of any given tensorial field theory. Requiring invariance of the gravitational dynamics under spacetime diffeomorphisms leads to a PDE system…

Gravitational theories with fixed background fields break diffeomorphism invariance. This breaking can be spontaneous or explicit. A brief summary of the main consequences of these types of breaking is presented.

Here show that, pure affine actions based solely on the Riemann curvature tensor lead to Einstein field equations for gravitation. The matter and radiation involved are general enough to impose no restrictions on material dynamics or vacuum…

We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might…

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…

After a preliminary discussion of the relevance of the field nature of gravitation interaction, both for the fundamental interaction of particles and the topology of space time, a method is proposed to produce and detect a dynamical…

After a preliminary discussion of the relevance of the field nature of gravitation interaction, both for the fundamental interaction of particles and the topology of space time, a method is proposed to produce and detect a dynamical…

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…

Local action principles on a manifold $\M$ are invariant (if at all) only under diffeomorphisms that preserve the boundary of $\M$. Suppose, however, that we wish to study only part of a system described by such a principle; namely, the…

Variational formalism in the extended phase space for fields is applied to gravity. It is shown that the requirement of invariance under arbitrary local inertial frames implies a coupling of torsion to a 3-form of matter fields on the one…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations,…

We continue to explore the possibility that the graviton in two dimensions is related to a quadratic differential that appears in the anomalous contribution of the gravitational effective action for chiral fermions. A higher dimensional…