Nicoleta Voicu

• Professor
• Professor (Full) at Transylvania University of Brașov

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.

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...

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...

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...

We investigate the gravitational field of a kinetic gas beyond its usual derivation from the second moment of the one-particle distribution function (1PDF), that serves as energy-momentum tensor in the Einstein equations. This standard procedure raises the question why the other moments of the 1PDF (which are needed to fully characterize the kinema...

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold...

The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity, since...

We locally classify all possible cosmological homogeneous and isotropic Landsberg-type Finsler structures, in 4-dimensions. Among them, we identify viable non-stationary Finsler spacetimes, i.e. those geometries leading to a physical causal structure and a dynamical universe. Noting that any non-stationary Landsberg metric must be actually non-Berw...

For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi–Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure; this property is known as Finsler (or Berwald–Finsler) metrizability. In the present paper, we clarify, for four...

The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity since o...

The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations – based on an intuitive “educated guess” – into the Euler–Lagrange one attached to a Lagrangian, by adding a canonical correction term. Here, we extend this technique to theories that involve at least two sets of dynami...

We clarify, for SO (3)-symmetric 4-dimensional Berwald-Finsler spaces of indefinite signature, the question of the existence of an affinely equivalent pseudo-Riemannian metric. It turns out that the answer depends on the holonomy distribution of the canonical affine connection and on the symmetry of its Ricci tensor. In particular, we find all clas...

The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations-based on an intuitive "educated guess"-into the Euler-Lagrange one attached to a Lagrangian, by adding a canonical correction term. Here, we extend this technique to theories that involve at least two sets of dynamical...

Finsler spacetime geometry is a canonical extension of Riemannian spacetime geometry. It is based on a general length measure for curves (which does not necessarily arise from a spacetime metric) and it is used as an effective description of spacetime in quantum gravity phenomenology as well as in extensions of general relativity aiming to provide...

Finsler spacetime geometry is a canonical extension of Riemannian spacetime geometry. It is based on a general length measure for curves (which does not necessarily arise from a spacetime metric) and it is used as an effective description of spacetime in quantum gravity phenomenology as well as in extensions of general relativity aiming to provide...

For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future-pointing time-like vectors is...

For the general class of pseudo-Finsler spaces with $(\alpha,\beta)$-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future pointing timelike ve...

We locally classify all [Formula: see text]-invariant four-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or [Formula: see text])-spherically symmetric pseudo-Riemannian ones — and serve as ansatz to find solutions of Finsler gravity equations which generalize the Einstein equations....

We locally classify all SO(3)-invariant 4-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or SO(3))-spherically symmetric pseudo-Riemannian ones - and serve as ansatz to find solutions of Finsler gravity equations which generalize the Einstein equations. We find that there exist six cl...

The thesis was submitted to Transilvania University of Brasov. Its full text can be found at: https://unitbv.ro/documente/cercetare/doctorat-postdoctorat/abilitare/teze-de-abilitare/voicu-nicoleta/05-Voicu-teza-abilitare-ENG.pdf

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...

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...

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...

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...

General Relativity and the ΛCDM 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 to be de...

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...

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...

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...

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...

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)....

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...

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,...

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...

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...

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...

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...

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...

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...

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...

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...

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 which reduces a series of problems involving ps...

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...

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...

This chapter is devoted to the discussion of various aspects of variational completion theory, with a special focus on applications in general relativity.

A revised version is available under the name of "Volume forms for Finsler spacetimes",

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...

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...

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...

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...

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...

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.

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...

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...

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.

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...

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...

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.

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...

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.

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...

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.

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.

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...

R. Miron and Gh. Atanasiu wrote the Einstein equations of a metric structure G on the tangent bundle T 2 M of order two, endowed with a nonlinear connection N and a linear connection D such that the 2-tangent structure J is absolutely parallel with respect to D. In the present paper, the authors determine the Einstein equations, by making use of th...

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...

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...

We determine the Bianchi identities for the d-torsions and d-curvatures of a distinguished liniar connection in the geometry of the second order.

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...

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.