Non-abelian Yang-Mills in Kundt spacetimes

We present new exact solutions of the Einstein-Yang-Mills system. The solutions are described by a null Yang-Mills field in a Kundt spacetime. They generalize a previously known solution for a metric of $pp$ wave type. The solutions are formally of Petrov type III.Comment: Talk presented at the XXVIII Spanish Relativity Meeting E.R.E. 2005, Oviedo, September 6-10, 2005, to be published by AIP Conference Proceedings, 5 page

Berwald spacetimes and very special relativity

In this work we study Berwald spacetimes and their vacuum dynamics, where the latter are based on a Finsler generalization of the Einstein's equations derived from an action on the unit tangent bundle. In particular, we consider a specific class of spacetimes which are non-flat generalizations of the very special relativity (VSR) line element, to which we refer as very general relativity (VGR). We derive necessary and sufficient conditions for the VGR line element to be of Berwald type. We present two novel examples with the corresponding vacuum field equations: a Finslerian generalization of vanishing scalar invariant (VSI) spacetimes in Einstein's gravity as well as the most general homogeneous and isotropic VGR spacetime.Comment: 17 pages, example section updated, journal references adde

On the non metrizability of Berwald Finsler spacetimes

We investigate whether Szabo's metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern-Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi-Civita connection of some Riemannian metric. We show for the first time that this result does not extend to Finsler spacetimes. More precisely, we find a large class of Berwald spacetimes for which the Ricci tensor of the affine connection is not symmetric. The fundamental difference from positive definite Finsler spaces that makes such an asymmetry possible, is the fact that generally, Finsler spacetimes satisfy certain smoothness properties only on a proper conic subset of the slit tangent bundle. Indeed, we prove that when the Finsler Lagrangian is smooth on the entire slit tangent bundle, the Ricci tensor must necessarily be symmetric. For large classes of Finsler spacetimes, however, the Berwald property does not imply that the affine structure is equivalent to the affine structure of a pseudo-Riemannian metric. Instead, the affine structure is that of metric-affine geometry with vanishing torsion.Comment: 12 pages, contribution to the Special Issue "Finsler Modification of Classical General Relativity" in the Journal Univers

Finsler gravitational waves of (α,β)(\alpha,\beta)-type and their observational signature

We introduce a new class of $(\alpha,\beta)$-type exact solutions in Finsler gravity closely related to the well-known pp-waves in general relativity. Our class contains most of the exact solutions currently known in the literature as special cases. The linearized versions of these solutions may be interpretted as Finslerian gravitational waves, and we investigate the physical effect of such waves. More precisely, we compute the Finslerian correction to the radar distance along an nterferometer arm at the moment a Finslerian gravitational wave passes a detector. We come to the remarkable conclusion that the effect of a Finslerian gravitational wave on an interferometer is indistinguishable from that of standard gravitational wave in general relativity. Along the way we also physically motivate a modification of the Randers metric and prove that it has some very interesting properties

Identifying Berwald Finsler Geometries

Berwald geometries are Finsler geometries close to (pseudo)-Riemannian geometries. We establish a simple first order partial differential equation as necessary and sufficient condition, which a given Finsler Lagrangian has to satisfy to be of Berwald type. Applied to $(\alpha,\beta)$-Finsler spaces, respectively $(A,B)$-Finsler spacetimes, this reduces to a necessary and sufficient condition for the Levi-Civita covariant derivative of the defining $1$-form. We illustrate our results with novel examples of $(\alpha,\beta)$-Berwald geometries which represent Finslerian versions of Kundt (constant scalar invariant) spacetimes. The results generalize earlier findings by Tavakol and van den Bergh, as well as the Berwald conditions for Randers and m-Kropina resp. very special/general relativity geometries.Comment: 17 pages, results on $(\alpha,\beta)$-Finsler geometries extended, explicit examples added, updated to journal versio

Randers pp-waves

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer and Wohlfarth's vacuum field equation of Finsler gravity for this class. We show that in this case the field equation is equivalent to the vanishing of the Finsler Ricci tensor, analogously to Einstein gravity. This implies that the considered vacuum field equation and Rutz's equation coincide in this scenario. We also construct all exact solutions of Berwald-Randers type to vacuum Finsler gravity, which turn out to be composed of a CCNV (covariantly constant null vector) Lorentzian spacetime, commonly known as pp-wave, and a 1-form given by the pp-wave distinguished null vector. We therefore refer to the found solutions as \textit{Randers pp-waves}.Comment: 11 pagers, updated to journal versio

Type III Einstein-Yang-Mills solutions

We construct two distinct classes of exact type III solutions of the D=4 Einstein-Yang-Mills system. The solutions are embeddings of the non-abelian plane waves in spacetimes in Kundt's class. Reduction of the solutions to type N leads to generalized $pp$ and Kundt waves. The geodesic equations are briefly discussed.Comment: revtex, 4 pages, minor changes, some factors and references corrected, footnote adde

A Cosmological Unicorn Solution to Finsler Gravity

We present a new family of exact vacuum solutions to Pfeifer and Wohlfarth's field equation in Finsler gravity, consisting of Finsler metrics that are Landsbergian but not Berwaldian, also known as unicorns due to their rarity. Interestingly we find that these solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. We furthermore find a promising analogy between our solutions and classical FLRW cosmology. One of our solutions in particular has cosmological symmetry, i.e. it is spatially homogeneous and isotropic, and it is additionally conformally flat, with conformal factor depending only on the timelike coordinate. We show that this conformal factor can be interpreted as the scale factor, we compute it as a function of cosmological time, and we show that it corresponds to a linearly expanding (or contracting) Finsler universe

Studio de la bioactividad potencial de extractos hemicelulósicos de la cascarilla de arroz

[ES] La cascarilla de arroz es un subproducto agroalimentario cuya revalorización tiene gran interés en el contexto de la economía circular. Es un material lignocelulósico con una importante fracción de hemicelulosas formada por arabinoxilanos sustituidos cuya ruptura da lugar a xilooligomeros con aplicaciones alimentarias, médicas y farmacéuticas. En este sentido, se han estudiado diversas metodologías que permitan la extracción de dichos compuestos a partir de subproductos de la industria alimentaria como la extracción alcalina y la extracción con agua subcrítica. A diferencia del proceso alcalino, la extracción con agua subcrítica no solo es una tecnología sostenible medioambientalmente, sino que además mantiene la funcionalidad de las fracciones hemicelulósicas aisladas de la materia prima. En este contexto resulta interesante la valorización de hemicelulosas a partir de cascarilla de arroz mediante ambas tecnologías a fin de poder comprar su funcionalidad en términos de actividad antioxidante y poder antimicrobiano. Este estudio contempla la determinación de la potencial actividad antioxidante de los diferentes extractos, así como el estudio de su potencial actividad antimicrobiana frente a bacterias tanto Gram – como Gram +. Para la determinación de la actividad antioxidante se ha utilizado el método de reducción del radical libre 2,2-difenil-1-picrilhidracilo (DPPH), lo cual permite comparar el poder antioxidante de ambos extractos con compuestos antioxidantes de referencia. En cuanto a la potencial actividad antimicrobiana de los extractos, se ha determinado la concentración mínima inhibitoria de ambos productos mediante el ensayo MTT que permite probar múltiples concentraciones diferentes al mismo tiempo de forma rápida y sencilla. De esta forma, se obtenido la información necesaria para su futura aplicación tanto en materiales de envasado de alimentos, como en la propia formulación de alimentos, ya que por sus propiedades activas permitirían prolongar su vida útil a la vez que se enriquecen en compuestos antioxidantes.[EN] Rice Husk is an agro-food by-product whose valorization is of great interest in the context of the circular economy. It is a lignocellulosic material with an important fraction of hemicelluloses constituted by substituted arabinoxylans whose rupture, gives rise to Xilo-oligomers with alimentary, medical and pharmaceutical applications. In this sense, several methodologies have been studied for allowing the extraction of these compounds from food industry byproducts, such as alkaline extraction and subcritical water extraction. Unlike the alkaline process, the extraction with subcritical water is not only an environmentally sustainable technology, but also maintains the functionality of the hemicellulose fractions isolated from the raw material. In this context, the valorization of hemicelluloses from rice husks through both technologies is interesting to compare their effectiveness at maintaining the hemicellulose functionality in terms of the antioxidant activity and antimicrobial capacity. This study includes the determination of the potential antioxidant activity of the different extracts, as well as the study of their potential antimicrobial activity against both Gram (-) and Gram (+) bacteria. For the determination of the antioxidant activity the method of reduction of the free radical 2.2- diphenyl-1-Picrilhidracilo (DPPH) was used, which allow for comparing the antioxidant capacity of both extracts with other known antioxidant compounds. As concerns the antimicrobial activity of the extracts, the minimum inhibitory concentration of both products was determined by means of the MTT test, which allows fortesting multiple different concentrations at the same time, in a quick and easy manner. In this way, the information necessary for its future application was obtained both in food packaging materials, as well as in food formulation, due to that fact that their active properties would allow for extending food shelf life, while food are enriched in antioxidant compounds.Almarche Fuster, A. (2018). Studio de la bioactividad potencial de extractos hemicelulósicos de la cascarilla de arroz. http://hdl.handle.net/10251/107252TFG

A simplified algorithm for inverting higher order diffusion tensors

In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann-Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI). An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI) data, one can estimate the diffusion orientation distribution function (dODF), which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor) to directly generalize the (second order) diffusion tensor approach. To enable efficient computation of Riemann-Finslerian quantities on diffusion weighted (DW)-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.</p