arXiv subjects

Alcides Garat

Publications and source records attributed to Alcides Garat.

At least 19 recordsLinked to original sources

arXiv2026

Full spacetime inversion generated by electromagnetic Abelian gauge transformations

In a previous manuscript we addressed the possibility of generating a reflection in a region of spacetime inside a null surface under electromagnetic gauge transformations. In this manuscript we will deal with the possibility of full inversions in a region of spacetime inside a null surface under electromagnetic gauge transformations. Since new tetrads whose construction depends on electromagnetic gauge were introduced it has been proved that the physical kinematic nature of spacetime can be altered as proved previously. In this case we will see how to create a field configuration that will reverse the flow of time. We will prove that we can turn a future directed timelike vector into a past directed timelike vector by physical means. Experiments devised in order to achieve time reversal or full inversion have been never discussed before.

gr-qc↗

arXiv2026

New symmetry in higher curvature spacetimes

New symmetries have been found in Einstein-Maxwell spacetimes. New symmetries have also been found in imperfect fluid curved spacetimes. We will prove in this paper that we can extend these symmetries to spacetimes with higher curvature terms. Higher curvature theories are in many cases associated to dark energy for instance. We provide further justification for these higher curvature formulations through the existence of a new symmetry.

physics.gen-ph↗

arXiv2026

Symmetry evolution for the imperfect fluid under perturbations

Ever since a new symmetry was found for the imperfect fluid with vorticity the question of the effect of perturbations on the symmetry itself has been raised. This new symmetry arose when realizing that local four-velocity gauge-like transformations would render the left hand side of the Einstein equations invariant. Because the metric tensor would be invariant under this new kind of local transformations. Then the point was raised about the invariance of such a kind of transformations of the stress-energy tensor on the right hand side of the Einstein equations in curved four-dimensional Lorentz spacetimes. It was verified that these invariances do not work with plain perfect fluids but they do work for imperfect fluids. The imperfect fluid stress-energy tensor will be invariant under local four-velocity gauge-like transformations when additional transformations are introduced for several variables included in the stress-energy tensor itself. This local invariance was also the criteria introduced in order to present a new stress-energy tensor for vorticity as well. New tetrads are at the core of the realization of the existence of this new symmetry because it is through these new tetrads that this new symmetry is realized. In this manuscript we will introduce local perturbations by external agents to the relevant objects in the imperfect fluid geometry. We will demonstrate a theorem that proves that the symmetries under four-velocity gauge-like transformations will be instantaneously broken but at the same time transformed into new symmetries. Because the local orthogonal planes determined by these new tetrads, which happen to be the local planes of symmetry will tilt under local perturbations. There will be a symmetry evolution under perturbations.

gr-qc↗

arXiv2026

Tetrads in SU(N) Yang-Mills geometrodynamics

The discovery of the SU(3) symmetry was fundamental as to establishing an ordering principle in particle physics. We already studied how to couple the SU(3) symmetry to the gravitational field in four-dimensional curved Lorentzian spacetimes. The multiplets of equal quantum numbers are translated through natural elements in Riemannian geometry into local multiplets of equal gravitational field. As quark physics developed since the seventies, it was necessary to incorporate new symmetries to the models, that ensued in the incorporation of new quantum numbers like Charm, for example. Charm is an additive quantum number like isospin T3 and hypercharge Y and the standard T3-Y diagrams were extended onto another third axis. Then, instead of the fundamental triplet we have a quartet {u; d; s; c} as the smallest representation of the symmetry group, leading to the introduction of SU(4) as the new group of symmetries. In this paper we will not restrict ourselves exclusively to the symmetry group SU(4) and we will set out to analyze the coupling of the SU(N) symmetry to the gravitational field. To this end new tetrads will be introduced as we did for the SU(3) x SU(2) x U(1) case. These tetrads have outstanding properties that enable these constructions. New theorems will be proved regarding the isomorphic nature of these local symmetry gauge groups and tensor products of groups of local tetrad transformations. This is a paper about grand field uni?fication in four-dimensional curved Lorentzian spacetimes.

gr-qc↗

arXiv2026

Isomorphism between the local Poincare generalized translations group and the group of spacetime transformations (x LB1)4

We will prove that there is a direct relationship between the Poincare subgroup of translations, and the group of tetrad transformations LB1 introduced in a previous manuscript. LB1 is the group composed by SO(1; 1) plus two kinds of discrete transformations. Translations have been extensively studied under the scope of gauge theories. By using the geometric structures built to prove this elementary result we will generalize it to the case of what we might call local translations. A special case of the latter is the Bondi-Metzner-Sachs subgroup of supertranslations. In order to accomplish this goal and since the group of translations is four-dimensional we will prove first that it is isomorphic to (x LB1)4. In order to prove this claim we will introduce a system of differential equations involving several kinds of fields. Abelian, non-Abelian, spinor, gravitational. These fields will constitute the structure needed to build local tetrads of a new kind that allow for the proof to be carried out with simplicity. Results already obtained involving similar but not equal tetrads will be useful in our constructions and demonstrations. Translations and generalized translations isomorphic to tensor products of LB1 groups are not trivial results. Because the LB1 group is composed by SO(1; 1) and two discrete transformations.

gr-qc↗

arXiv2026

Singular gauge transformations in geometrodynamics

The new tetrads introduced previously for non-null electromagnetic fields in Einstein- Maxwell spacetimes enable a direct link to the local electromagnetic gauge group of transformations. Due to the peculiar elements in the construction of these new tetrads a direct connection can be established between the local group of electromagnetic gauge transformations and local groups of tetrad transformations on two different local and orthogonal planes of eigenvectors of the Einstein-Maxwell stress-energy tensor. These tetrad vectors are gauge dependent. It is an interesting and relevant problem to study if there are local gauge transformations that can map on the timelike-spacelike plane, the timelike and the spacelike vectors into the intersection of the local light cone and the plane itself. How many of these local gauge transformations exist and how the mathematics and the geometry of these particular transformations play out. These local gauge transformations would be singular and it is important to identify them.

gr-qc↗

arXiv2026

New symmetry for the imperfect fluid

We will address the existence of a new symmetry for an imperfect fluid by introducing local four-velocity gauge-like transformations for the case when there is vorticity. A similar tetrad formulation as to the Einstein-Maxwell spacetimes formalism presented in previous manuscripts will be developed in this manuscript for the imperfect fluids. The four-velocity curl and the metric tensor will be invariant under these kind of four-velocity gauge-like local transformations. While the Einstein-Maxwell stress-energy tensor is locally gauge invariant under electromagnetic gauge transformations, the perfect fluid stress-energy tensor will not be invariant under four-velocity gauge-like local transformations. We will dedicate our analysis to the imperfect fluid stress-energy tensor that will be invariant under local four-velocity gauge-like transformations when additional transformations are introduced for several variables included in the stress-energy tensor itself. We will also pay special attention to the construction of a vorticity stress-energy tensor invariant under local four-velocity gauge-like transformations. An application on neutron stars will be developed in order to show the simplifications brought about by these new tetrads.

gr-qc↗

arXiv2013

On the nature of the new group LB1

The new local group LB1 introduced previously will be studied and reviewed in detail, depicting its unique nature that makes it a new group in fundamental physics. It will be made clear that even though most of its elements are Lorentz transformations, one unique discrete transformation not present in the Lorentz groups, is making this group into a new group because it is a reflection. In addition there will be four particular transformations onto the local light cone. It is these discrete transformations that allow for an isomorphism between the group U(1) and LB1. This result will have profound resonations in all of particle physics, general relativity, relativistic astrophysics, Riemannian geometry and group theory. These new group will be associated to a whole set of new experiments put forward.

physics.gen-ph↗

arXiv2013

Dynamical symmetry breaking in Yang-Mills geometrodynamics

We will analyze through a first order perturbative formulation the local loss of symmetry when a source of non-Abelian Yang-Mills and gravitational fields interacts with an external agent that perturbes the original geometry associated to the source. Then, as the symmetry in Abelian and non-Abelian field structures in four-dimensional Lorentzian spacetimes is displayed through the existence of local planes of symmetry that we previously called blades one and two. These orthogonal local planes diagonalize the stress-energy tensor and every vector in these planes is an eigenvector of the stress-energy tensor. The loss of symmetry will be manifested by the tilting of these planes under the influence of the external agent. It was also found already that there is an algorithm to block diagonalize the Yang-Mills field strength in a local gauge invariant way. The loss of symmetry will also be manifested by the tilting of these planes that block diagonalize the Yang-Mills field strength under the influence of the external agent. As the interaction proceeds, the planes will tilt perturbatively, and in this strict sense the original local symmetry will be lost. But we will prove that the new orthogonal planes or blades at the same point will correspond after the tilting generated by perturbation to a new symmetry, with associated new local currents, both on each new local planes of symmetry. Old symmetries will be broken, new symmetries will arise. There will be a local symmetry evolution in the non-Abelian case as well. This result will produce a new theorem on dynamic symmetry evolution. This new classical model will be useful in order to better understand anomalies in quantum field theories.

gr-qc↗

arXiv2013

The equivalence between local inertial frames and electromagnetic gauge in Einstein-Maxwell theories

It has been proven that locally the inertial frames and gauge states of the electromagnetic field are equivalent. This proof is valid for Einstein-Maxwell theories in four-dimensional Lorentzian spacetimes. Use will be made of theorems proved in a previous manuscript. These theorems state that locally the group of electromagnetic gauge transformations is isomorphic to the local group of Lorentz transformations of a special set of tetrad vectors. The tetrad that locally and covariantly diagonalizes any non-null electromagnetic stress-energy tensor. Two isomorphisms, one for each orthogonal plane of stress-energy eigenvectors. We will discuss the opposite problem in this paper. What happens with local electromagnetic gauge when the test object under study is boosted by any mechanical means. We will prove that boosting matter is indistinguishable from introducing an appropriate local electromagnetic gauge transformation.

gr-qc↗

arXiv2013

The Monopole and the Coulomb field as duals within the unifying Reissner-Nordstrom geometry

We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner-Nordstrom spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner-Nordstrom geometry.

gr-qc↗

arXiv2013

Euler observers in geometrodynamics

Euler observers are a fundamental tool for the study of spacetime evolution. Cauchy surfaces are evolved through the use of hypersurface orthogonal fields and their relationship to coordinate observers, that enable the use of already developed algorithms. In geometrodynamics new tetrad vectors have been introduced with outstanding simplifying properties. We are going to use these already introduced tetrad vectors in the case where we consider a curved four dimensional Lorentzian spacetime with the presence of electromagnetic fields. These Einstein-Maxwell geometries will provide the new tetrad that we are going to use in order to develop an algorithm to produce Cauchy evolution with additional simplifying properties.

gr-qc↗

arXiv2013

Gauge invariant method for maximum simplification of the field strength in non-Abelian Yang-Mills theories

A new local gauge invariant method is introduced in order to maximally simplify the expression for a SU(2) non-Abelian field strength. The new tetrads introduced in previous works are going to play a fundamental role in the algorithm presented in this manuscript. Three new local gauge invariant objects are going to guide us through the process of making a field strength block diagonal. The process is also covariant. Any non-trivial isospace field strength projection will become block diagonal through this gauge invariant algorithm. As an application we will find new local observables in Yang-Mills theories.

gr-qc↗

arXiv2013

Dynamical symmetry breaking in geometrodynamics

We will analyze through a first order perturbative formulation the local loss of symmetry when a source of electromagnetic and gravitational field interacts with an agent that perturbs the original geometry associated to the source. As the local gauge symmetry in Abelian or even non-Abelian field structures in four-dimensional Lorentzian spacetimes is displayed through the existence of local planes of symmetry that we will refer to as blades one and two, the loss of symmetry will be manifested by the tilting of these planes under the influence of an external agent. In this strict sense the original local symmetry will be lost. We will be able to prove in this way that the new blades at the same point will correspond ''after the tilting generated by perturbation" to a new symmetry. The purpose of this paper is to show that the geometrical manifestation of local gauge symmetries is dynamic. Despite the fact that the local original symmetries will be lost, new symmetries will arise. A dynamic evolution of local symmetries will be evidenced. This result will produce a new theorem on dynamic symmetry evolution.

gr-qc↗

arXiv2012

Covariant diagonalization of the perfect fluid stress-energy tensor

We introduce new tetrads that manifestly and covariantly diagonalize the stress-energy tensor for a perfect fluid with vorticity at every spacetime point. This new tetrad can be applied and introduce simplification in the analysis of astrophysical relativistic problems where vorticity is present through the Carter-Lichnerowicz equation. This new tetrad also enables the construction in a simple fashion of Euler and Coordinate observers relevant to the Cauchy evolution of many hydrodynamical relativistic problems in the case with no vorticity and the presence of a symmetry where the tetrads are completely analogous to the case with vorticity. We also discuss the origin of inertia in this special case from the standpoint of our new local tetrads.

gr-qc↗

arXiv2012

Second proof for SU(2) isomorphic to LB1 X LB1 X LB1 theorem

In this note we present a second independent proof for the theorem introduced previously that establishes an isomorphism between SU(2) and LB1 X LB1 X LB1. Since the local groups LB1 and LB2 are isomorphic, it was also previously proved a similar result for LB2 X LB2 X LB2. We are going to reverse the three sets of tetrads that are going to be used in order to prove this new version. Instead of choosing three SU(2) different tetrads keeping the electromagnetic tetrad the same for all three sets of SU(2) tetrads, we are going to keep fixed the SU(2) tetrad, that is, we are going to pick just one SU(2) tetrad but choose three different arbitrary but fixed electromagnetic tetrads in order to gauge locally the only local SU(2) tetrad involved in our new version of this theorem. The same result will be obtained via an alternative but equivalent way.

gr-qc↗

arXiv2012

Tetrads in SU(3) X SU(2) X U(1) Yang-Mills geometrodynamics

The relationship between gauge and gravity amounts to understanding underlying new geometrical local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and Non-Abelian in four-dimensional Lorentzian curved spacetimes. In the present manuscript a new tetrad is introduced for the Yang- Mills SU(3) x SU(2) x U(1) formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations that we previously called LB1 and LB2. New theorems are proved regarding isomorphisms between local internal SU(3) x SU(2) x U(1) groups and local tensor products of spacetime LB1 and LB2 groups of transformations. These new tetrads define at every point in spacetime two orthogonal planes that we called blades or planes one and two. These are the local planes of covariant diagonalization of the stress-energy tensor. These tetrads are gauge dependent. Tetrad local gauge transformations leave the tetrads inside the local original planes without leaving them. These local tetrad gauge transformations enable the possibility to connect local gauge groups Abelian or non-Abelian with local groups of tetrad transformations. These new tetrads have displayed manifestly and non-trivially the coupling between Yang-Mills fields and gravity. The new tetrads and the stress-energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang-Mills stress-energy tensor is developed as an application. This is a paper about grand Standard Model gauge theories - General Relativity gravity unification and grand group unification in four-dimensional curved Lorentzian spacetimes.

gr-qc↗

arXiv2012

The Lorentz force equation as Fermi-Walker transport in geometrodynamics

A new tetrad introduced within the framework of geometrodynamics for non-null electromagnetic fields allows for the geometrical analysis of the Lorentz force equation and its solutions in curved spacetimes. When expressed in terms of this new tetrad, the electromagnetic field displays explicitly maximum simplification, and the degrees of freedom are manifestly revealed. In our manuscript we are deducing the Lorentz force equation on purely Riemannian geometrical grounds. The equation arises on the basis of Frenet-Serret analysis through the use of our new tetrads and gauge invariance arguments only. The force is deduced through a geometrical construction that precludes any other mathematical form other than the one already accepted. Therefore, a significant and fundamental result such as the first geometrical proof on the necessity of the force in the equation to have the structure already accepted in physics and not any other, is given. Through the use of the Frenet-Serret formulae and gauge invariance arguments we are also able to express in terms of the new tetrad vectors the Lorentz force equation as a generalized form of Fermi-Walker transport.

gr-qc↗