Related papers: Gauge and constraint degrees of freedom: from anal…
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…
We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data.…
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
The "Newtonian" or non-relativistic decomposition of Einstein's gravitational field is useful in the post-Newtonian approximation. We obtain the full non-quadratic Einstein-Hilbert action in terms of these fields as well as the harmonic…
$3+1$ formulations of the Einstein field equations have become an invaluable tool in Numerical relativity, having been used successfully in modeling spacetimes of black hole collisions, stellar collapse and other complex systems. It is…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
We find a choice of variables for the 3+1 formulation of general relativity which casts the evolution equations into (flux-conservative) symmetric-hyperbolic first order form for arbitrary lapse and shift, for the first time. We redefine…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
A general covariant extension of Einstein's field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector. The extended field equations,…
To appear in proceedings of II Workshop on ``Constraints Theory and Quantisation Methods''Montepulciano (Siena) 1993} General discussion of the constraints of 2+1 gravity, with emphasis on two approaches, namely the second order and first…
Classically the constraint algebra of general relativity, which generates gauge transformations, is equivalent to spacetime covariance. In LQG, inverse triad corrections lead to an effective Hamiltonian constraint which can lead to a…
We consider a specific Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, where the canonical variables are expressed by means of differential forms. We show that some ``position'' variables of this formulation…
This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…