Related papers: Linear Form of Canonical Gravity
Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…
Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle.…
Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to…
Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
We give the most general conditions to date which lead to uniqueness of the general relativistic Hamiltonian. Namely, we show that all spatially covariant generalizations of the scalar constraint which extend the standard one while…
Relativistic Coulomb systems are studied in velocity space, prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space provides a method much simpler (and more elegant) than the familiar analytic solutions in…
In this work, a method for solving the constraints of general relativity is presented, where first all geometrical objects are written in terms of a set of orthonormal triads and a flat Weitzenbock connection, which depends on the triads…
We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional, while an "internal" space is enlarged.…
Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\cal…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc.…
If two point particles collide relativistically in one dimension, and the masses, velocities and gamma factors of the incoming particles are rational numbers, then the velocities and gamma factors of the outgoing particles are rational.…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
Besides the String Theory context, the quantum General Relativity can be studied by the use of constrained topological field theories. In the celebrated Plebanski formalism, the constraints connecting topological field theories and gravity…
In this contribution we sketch a branch-cut quantum formulation of the Wheeler-DeWitt equation analytically continued to the complex plane. As a starting point, we base our approach on the Ho\v{r}ava-Lifshitz formulation of gravity, which…