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R. Tresguerres

Publications and source records attributed to R. Tresguerres.

11 recordsLinked to original sources
arXiv2006

Towards a general solution of the Hamiltonian constraints of General Relativity

The present work has a double aim. On the one hand we call attention on the relationship existing between the Ashtekar formalism and other gauge-theoretical approaches to gravity, in particular the Poincaré Gauge Theory. On the other hand we study two kinds of solutions for the constraints of General Relativity, consisting of two mutually independent parts, namely a general three-metric-dependent contribution to the extrinsic curvature $K_{ab}$ in terms of the Cotton-York tensor, and besides it further metric independent contributions, which we analyze in particular in the presence of isotropic three-metrics.

gr-qc↗
arXiv2005

Gauge theories of gravity: the nonlinear framework

Nonlinear realizations of spacetime groups are presented as a versatile mathematical tool providing a common foundation for quite different formulations of gauge theories of gravity. We apply nonlinear realizations in particular to both the Poincaré and the affine group in order to develop Poincaré gauge theory (PGT) and metric-affine gravity (MAG) respectively. Regarding PGT, two alternative nonlinear treatments of the Poincaré group are developed, one of them being suitable to deal with the Lagrangian and the other one with the Hamiltonian version of the same gauge theory. We argue that our Hamiltonian approach to PGT is closely related to Ashtekar's approach to gravity. On the other hand, a brief survey on MAG clarifies the role played by the metric--affine metric tensor as a Goldsone field. All gravitational quantities in fact --the metric as much as the coframes and connections-- are shown to acquire a simple gauge--theoretical interpretation in the nonlinear framework.

gr-qc↗
arXiv2000

Gravitational Goldstone fields from affine gauge theory

In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric does not constitute any more an independent gravitational potential, since its degrees of freedom reveal to correspond to eliminable Goldstone bosons. This may be an important advantage for quantization.

gr-qc↗
arXiv1996

Time Evolution in Dynamical Spacetimes

We present a gauge--theoretical derivation of the notion of time, suitable to describe the Hamiltonian time evolution of gravitational systems. It is based on a nonlinear coset realization of the Poincaré group, implying the time component of the coframe to be invariant, and thus to represent a metric time. The unitary gauge fixing of the boosts gives rise to the foliation of spacetime along the time direction. The three supressed degrees of freedom correspond to Goldstone--like fields, whereas the remaining time component is a Higgs--like boson.

gr-qc↗
arXiv1996

An axially symmetric solution of metric-affine gravity

We present an exact stationary {\it axially symmetric} vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.

gr-qc↗
arXiv1996

An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges

The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses {\it nonmetricity} and {\it torsion} as post-Riemannian structures. The sources of MAG are the conserved currents of energy-momentum and dilation, shear and spin. We present an exact static spherically symmetric vacuum solution of the theory describing the exterior of a lump of matter carrying mass and dilation, shear and spin charges.

gr-qc↗
arXiv1996

Hamiltonian Poincaré Gauge Theory of Gravitation

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincaré group, taken as the local spacetime group of the gravitational gauge theory, with $SO(3)$ as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary $SO(3)$ vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.

gr-qc↗
arXiv1994

Ordinary Matter in Nonlinear Affine Gauge Theories of Gravitation

We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.

gr-qc↗
arXiv1994

Nonlinear Gauge Realization of Spacetime Symmetries Including Translations

We present a general scheme for the nonlinear gauge realizations of spacetime groups on coset spaces of the groups considered. In order to show the relevance of the method for the rigorous treatment of the translations in gravitational gauge theories, we apply it in particular to the affine group. This is an illustration of the family of spacetime symmetries having the form of a semidirect product $H\semidirect T$, where $H$ is the stability subgroup and $T$ are the translations . The translational component of the connection behaves like a true tensor under $H$ when coset realizations are involved.

gr-qc↗
arXiv1993

Towards complete integrability of two dimensional Poincaré gauge gravity

It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational {\it boundary} term. The resulting model is equivalent to a Yang-Mills theory of local {\it translations} and frozen Lorentz gauge degrees. We will show that this restricted Poincaré gauge model in 2 dimensions is completely integrable. {\it Exact} wave, charged black hole, and `dilaton' solutions are then readily found. In vacuum, the integrability of the {\it general} 2D Poincaré gauge theory is formally proved along the same line of reasoning.

hep-th↗