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A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
Variational Relativity is a framework developed by Souriau in the sixties to better formulate General Relativity and its classical limit\,: Classical Continuum Mechanics. It has been used, for instance, to formulate Hyperelasticity in…
We investigate the structure of equations of motion and lagrangian constraints in a general theory of massive spin 2 field interacting with external gravity. We demonstrate how consistency with the flat limit can be achieved in a number of…
Classical relativistic field theory is applied to perfect and magneto-hydrodynamic flows. The fields for Hamilton's principle are shown to be the Lagrangian coordinates of the fluid elements, which are potentials for the matter current…
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.
We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt…
Motivated by recent developments in the theory of gravitation, we revisit the idea of topological variations, originally introduced by Wheeler and Hawking, from a rigorous perspective. Starting from a localized version of the…
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…
Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory.…
A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most…
Euler-Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two-spheres. The geometric structure of a product of two-spheres is carefully considered in order to obtain global…
A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\to X$ are treated as classical…
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…
The Palatini formalism is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, but we follow a completely covariant approach by…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the derivatives of the…
Assuming the minimal time to send a bit of information in the Einstein clock synchronization of the two clocks located at different positions, we introduce the extended metric to the information space. This modification of relativity…