Nicoleta Voicu

Nicoleta Voicu
Universitatea Transilvania Brasov | unitbv · Department of Mathematics and Computer Sciences

PhD

About

56
Publications
6,181
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363
Citations
Introduction
Nicoleta Voicu currently works at the Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov. Nicoleta does research in Geometry, Applied Mathematics and Mathematical Physics. Their current project is 'Finsler-Kawaguchi methods in field theory'.
Additional affiliations
October 2014 - present
Universitatea Transilvania Brasov
Position
  • Professor (Associate)
June 2010 - May 2013
Universitatea Transilvania Brasov
Position
  • PostDoc Position

Publications

Publications (56)
Article
Full-text available
Given a non-variational system of differential equations, the simplest way of turning it into a variational one is by adding a correction term. In the paper, we propose a way of obtaining such a correction term, based on the so-called Vainberg-Tonti Lagrangian, and present several applications in general relativity and classical mechanics.
Article
Full-text available
The paper presents a general geometric approach to energy-momentum tensors in Lagrangian field theories, based on a Hilbert-type definition. The approach is consistent with the ones defining energy-momentum tensors in terms of hypermomentum maps given by the diffeomorphism invariance of the Lagrangian - and, in a sense, complementary to these, with...
Article
Full-text available
In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be a scalar equation. In th...
Article
Full-text available
We propose a new model for the description of a gravitating multiparticle system, viewed as a kinetic gas. The properties of the (colliding or noncolliding) particles are encoded into a so-called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e., on the tangent bundle of the space...
Article
Full-text available
This paper introduces a general mathematical framework for action-based field theories on Finsler spacetimes. As most often fields on Finsler spacetime (e.g., the Finsler fundamental function or the resulting metric tensor) have a homogeneous dependence on the tangent directions of spacetime, we construct the appropriate configuration bundles whose...
Article
Full-text available
Lepage equivalents of Lagrangians are a higher order, field-theoretical generalization of the notion of Poincaré-Cartan form from mechanics and play a similar role: they give rise to a geometric formulation (and to a geometric understanding) of the calculus of variations. A long-standing open problem is the determination, for field-theoretical Lagr...
Chapter
This chapter summarises some recent developments in the application of Finsler geometry as the extended geometry of spacetime. As original sources, we refer to the articles [1, 2, 3]. Finsler geometry appears in the description of physical systems, as a suitable mathematical tool at various stages. We will briefly discuss the appearance of Finsler...
Preprint
Full-text available
General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research...
Preprint
Full-text available
For field-theoretical Lagrangians of arbitrary order, we construct Lepage equivalents with the so-called closure property: the Lepage equivalent is a closed differential form if and only if its corresponding Lagrangian has vanishing Euler-Lagrange expressions. The construction is a local one; yet, we prove that in most of the cases of interest for...
Article
Full-text available
We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Aczel’s, Popoviciu’s and Bellman’s inequalities, are all particular cases of a reverse Cauchy-Schwarz, respectively, of a reverse...
Article
Full-text available
Recently, a proposal to obtain a finite contribution of second derivative order to the gravitational field equations in \(D = 4\) dimensions from a renormalized Gauss–Bonnet term in the action has received a wave of attention. It triggered a discussion whether the employed renormalization procedure yields a well-defined theory. One of the main crit...
Preprint
Full-text available
A proposal to obtain a finite contribution of second derivative order to the gravitational field equations in (D = 4) dimensions from a renormalized Gauss-Bonnet term in the action has recently received a wave of attention, and triggered a discussion whether the employed renormalization procedure yields a well-defined theory. One of the main critic...
Article
Full-text available
Abstract A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF)....
Preprint
Full-text available
We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Acz\'el's, Popoviciu's and Bellman's inequalities, are all particular cases of a reverse Cauchy-Schwarz, respectively, of a rever...
Preprint
A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF). However,...
Article
Full-text available
Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. In particular, we find the most general spatially homogeneous and isotropic Berwald spacetimes, which are Finsler spa...
Article
Full-text available
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...
Preprint
Berwald spacetimes are Finsler spacetimes that are closest to pseudo-Riemannian spacetime geometry. Applying the cosmological principle, we find the most general spatially homogeneous and isotropic Berwald spacetime geometries. They are defined by a Finsler Lagrangian built from a free function on spacetime and a zero-homogeneous function on the ta...
Preprint
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...
Preprint
Full-text available
We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the (colliding or non-colliding) particles are encoded into a so called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e. on the tangent bundle of the spac...
Preprint
Full-text available
We propose a new model for the description of a gravitating multi particle system, viewed as a kinetic gas. The properties of the, colliding or non-colliding, particles are encoded into a so called one-particle distribution function, which is a density on the space of allowed particle positions and velocities, i.e.\ on the tangent bundle of the spa...
Preprint
Full-text available
In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler geometry is based on a scalar function on the tangent bundle, the field equation which determines this function should also be scalar equation on the t...
Article
Full-text available
The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary for field-theoretical applications and by proposing a technique that reduces a series of problems involving pse...
Article
Full-text available
The paper proposes extensions of the notions of Busemann-Hausdorff and Holmes-Thompson volume to time orientable Finslerian spacetime manifolds. These notions are designed to also make sense in cases when the Fins- lerian metric tensors are either not defi…ned or degenerate along some di- rections in each tangent space - which is the case with the...
Article
Full-text available
Tangent fibrations generate a “multifloored tower”, while raising from one of its floors to the next one, one practically reiterates the previously performed actions. In this way, the “tower” admits a laddershaped structure. Raising to the first floors suffiices for iteratively performing the subsequent steps. The paper mainly studies the tangent f...
Chapter
This chapter is devoted to the discussion of various aspects of variational completion theory, with a special focus on applications in general relativity.
Article
A revised version is available under the name of "Volume forms for Finsler spacetimes",
Article
Full-text available
Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and various branches of computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, existence of non-geodesic biharmonic curves for some classes of...
Article
Full-text available
The notions of bienergy of a smooth mapping and of biharmonic map between Riemannian manifolds are extended to the case when the domain is Finslerian. We determine the first and the second variation of the bienergy functional, the equations of Finsler-to-Riemann biharmonic maps and some specific examples. Two notable results in Riemannian geometry...
Book
Full-text available
Differential prolongations are usually obtained by means of differentiation and jets of mappings which are, in a way or another, related to local coordinates. The present book sets the foundation of prolongation theory on iterated tangent bundles, in a coordinate-free manner. Lie-Cartan calculus, the theory of connections in bundles and certain spe...
Article
Full-text available
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompa...
Article
Full-text available
In 2008-2009, F. Costa and C. Herdeiro proposed a new gravito-electromagnetic analogy, based on tidal tensors. We show that connections on the tangent bundle of the space-time manifold can help not only in finding a covnenient geometrization of their ideas, but also a common mathematical description of the main equations of gravity and electromagne...
Article
Full-text available
To define a higher order connection on a fibered manifold one can use the sections of nonholonomic jet prolongations. However, a more natural approach seems to be the one assuming the structure of a higher-order tangent bundle and using White's sector-forms on these bundles.
Article
Full-text available
In a previous paper, we have introduced a new unified description of the main equations of the gravitational and of the electromagnetic field, in terms of tidal tensors and connections on the tangent bundle TM of the space-time manifold. In the present work, we relate these equations to variational procedures on the tangent bundle. The Ricci scalar...
Article
Full-text available
By using variational calculus and exterior derivative formalism, we proposed in two previous joint papers with S. Siparov a new geometric approach for electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge invariance. Also, for flat pse...
Article
Full-text available
We find a simple generalization of Einstein equations to pseudo-Finslerian spaces by variational means and, based on the invariance of the Finslerian Hilbert action to infinitesimal transformations, we find the analogue of the energy-momentum conservation law in these spaces.
Conference Paper
Full-text available
Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical equations of electromagnetism to anisotropic (Finslerian) spaces. The results differ from the ones obtained b...
Article
Some specific astrophysical data collected during the last decade suggest the need of a modification of the expression for the Einstein‐Hilbert action, and several attempts are known in this respect. The modification suggested in this paper stems from a possible anisotropy of space‐time—which leads to a dependence on directional variables of the si...
Article
Full-text available
We find the generalization of Einstein equations to Finsler spaces by variational means and, based on the invariance of the Finslerian Hilbert action to infinitesimal transformations, we find the analogue of the energy- momentum conservation law in these spaces.
Article
Some specific astrophysical data collected during the last decade cause a need of modifications in the expression of the Einstein-Hilbert action, and several attempts sufficing this need are known. Most of them deal with the direct (and in a sense arbitrary) modification of the "simplest scalar". In this paper, we investigate the situation when the...
Article
Full-text available
We show that anisotropy of the space naturally leads to new terms in the expression of Lorentz force, as well as in the expressions of currents.
Article
Full-text available
The specific astrophysical data collected during the last decade causes the need for the modification of the expression for the Einstein-Hilbert action, and several attempts sufficing this need are known. The modification suggested in this paper stems from the possible anisotropy of space-time and this means the natural change of the simplest scala...
Article
Full-text available
For Finsler spaces (M,F) endowed with m-th root metrics, we provide necessary and sufficient conditions in which they are projectively flat, or projectively related to Berwald/Riemann spaces. We also give a specific characterization for m-th root metrics spaces of Landsberg and of Berwald type.
Article
Full-text available
We show that, for mechanical system with external forces, the equations of deviations of solution curves of the corresponding Lagrange equations,determine a nonlinear connection on the second order osculator (second order tangent) bundle. In particular, Jacobi equations in Finsler and Riemann spaces determine such a nonlinear connection.
Article
Full-text available
The paper determines basic relations between the metric canonically induced by the Berwald-Moor Finsler structure, the normalized flag generalized Lagrange metric and the Pavlov poly-scalar product. Then, in the framework of vector bundles endowed with (h,v)-metrics, the extended Einstein equations are obtained for both the associated generalized L...
Article
Full-text available
In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent...
Article
Full-text available
The basic types of curves on jet spaces endowed with non-linear connection (namely, the h-paths, v-paths, stationary curves and geodesics) are characterized. The main geometric objects and the paths of the framework are described and, in the special case when the vertical metric is independent of fiber coordinates, the first variation of energy is...
Article
We determine the Bianchi identities for the d-torsions and d-curvatures of a distinguished liniar connection in the geometry of the second order.
Article
Full-text available
In two previous papers, we proposed a new unified mathematical description of the main equations of gravity and electromagnetism, based on Finslerian connections on the tangent bundle of the space-time manifold and on tidal tensors. In the present paper, we present these results and point out the relations between the obtained geo-metric objects an...
Article
Full-text available
On a Riemannian manifold endowed with a metrical linear connection with nonvanishing torsion, there are computed the first and second variation of energy and there is proven that the main results related to geodesics and Jacobi fields known for the Levi-Civita connection (including Morse's index theorem), hold true also in this case.

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Projects

Project (1)
Project
We aim to construct solid mathematical foundations of a Finslerian extension of general relativity, together with a generalization of variational principles to higher order Grassmann fibrations.