arXiv subjects

Lehel Csillag

Publications and source records attributed to Lehel Csillag.

10 recordsLinked to original sources

arXiv2026

Exact black hole solutions with semi-symmetric vectorial torsion

Semi-Symmetric metric gravity extends general relativity by introducing a semi-symmetric connection with vectorial torsion. The modified field equations contain extra contributions from the torsion vector and its derivatives. Assuming a purely radial torsion vector consistent with spherical symmetry, we derive two exact vacuum solutions. The metric depends on two integration constants, defining the Schwarzschild radius and a new cosmological-type length scale. Classical Solar System tests, including perihelion precession, light deflection, and radar echo delay, are used to constrain the new length scale and the associated deviations from general relativity. The thermodynamic properties of the resulting black hole solutions are investigated, and it is shown that the vector perturbation sector is linearly stable.

gr-qc↗

arXiv2026

On the Finsler variational nature of autoparallels in metric-affine geometry

In metric-affine geometry, autoparallels are generically non-variational, i.e., they are not the extremals of any action integral. The existence of a parametrization-invariant action principle for autoparallels is a long-standing open problem, which is equivalent to the so-called Finsler metrizability of the connection -- that is, to the fact that these autoparallels can be interpreted as Finsler geodesics. In this article, we address this problem for the class of torsion-free affine connections with vectorial nonmetricity, which includes, as notable subcases, Weyl and Schrödinger connections. For this class, we determine the necessary and sufficient conditions for the existence of a Finsler Lagrangian that metrizes the connection (and depends only algebraically on the metric and on the nonmetricity defining vector field). In the cases where such a Finsler Lagrangian exists, we construct it explicitly. In particular, we show that a broad class of such connections is in fact Finsler metrizable, i.e., the autoparallels of these connections are Finsler geodesics.

math-ph↗

arXiv2026

Herglotz-type $f(R,T)$ gravity

The non-conservation of the energy-momentum tensor in $f(R,T)$ gravity can be interpreted as an effective manifestation of dissipation. Motivated by this, we propose a new formulation of $f(R,T)$ gravity based on the Herglotz variational principle, which extends the usual {Hamilton} variational principle to dissipative systems by allowing the Lagrangian to depend explicitly on the action. The resulting gravitational field equations extend those of $f(R,T)$ gravity by including Herglotz contributions. In the Newtonian limit, these contributions modify the gravitational potential, allowing us to constrain the Herglotz vector through Mercury's perihelion precession and the relativistic light deflection. The Herglotz corrections lead to a scaling law consistent with observations from the Cassini spacecraft. Examining two representative cosmological models, the Herglotz vector effectively reduces to a single function that, under suitable conditions, can play the role of a cosmological constant, providing an alternative mechanism for the Universe's accelerated expansion. Within the Herglotz variational approach, the linear $f(R,T)=R+αT$ model, previously ruled out in the standard formulation due to its fixed deceleration parameter, becomes consistent with observations {for a certain choice of the Herglotz vector.

gr-qc↗

arXiv2025

From Barthel Randers Kropina Geometries to the Accelerating Universe: A Brief Review of Recent Advances in Finslerian Cosmology

We review recent developments in cosmological models based on Finsler geometry and extensions of general relativity within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend on position and an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We explore whether Finsler-type geometries can describe gravitational interaction and cosmological dynamics. In particular, we examine the Barthel connection and $(α, β)$ geometries, where $α$ is a Riemannian metric and $β$ is a one-form. For a specific construction of $β$, the Barthel connection coincides with the Levi-Civita connection of the associated Riemann metric. We review gravitational field and cosmological evolution in three geometries: Barthel-Randers ($F = α+ β$), Barthel-Kropina ($F = α^2 β$), and the conformally transformed Barthel-Kropina geometry. After presenting the mathematical foundations of Finslerian-type modified gravity theories, we derive generalized Friedmann equations in these geometries assuming a Friedmann-Lemaître-Robertson-Walker type metric. We also present the matter-energy balance equations, interpreting them from the perspective of thermodynamics with particle creation. The cosmological properties of Barthel-Randers and Barthel-Kropina models are explored in detail. The additional geometric terms in these models can be interpreted as an effective dark energy component, generating an effective cosmological constant. Several cosmological solutions are compared with observational data (Cosmic Chronometers, Type Ia Supernovae, Baryon Acoustic Oscillations) using MCMC analysis. A comparison with the $Λ$CDM model shows that Finslerian models fit observational data well, suggesting they offer a viable alternative to general relativity.

gr-qc↗

arXiv2025

Geometric formulation of $k$-essence and late-time acceleration

We study a class of geometries in which nonmetricity is fully determined by a vectorial degree of freedom and three independent coefficients. Formulating the simplest linear action in this geometry, implemented through Lagrange multipliers, naturally leads to an equivalence with the purely kinetic $k$-essence models with quadratic kinetic terms. A detailed dynamical systems analysis reveals that the $\Lambda$CDM phenomenology is embedded within the model. Crucially, we find that if stability conditions such as a positive sound speed squared and energy density are not enforced, the model generically exhibits instabilities and divergent behaviour in the phase space. These physical viability criteria allow us to isolate stable regions of the parameter space and derive well-motivated priors for parameter inference. Using Markov Chain Monte Carlo methods and late-time observational data, including cosmic chronometers, Pantheon$^{+}$ Type Ia supernovae, and DESI baryon acoustic oscillations, we constrain the degrees of freedom associated with nonmetricity and demonstrate the viability of the model. We discuss the implications of these results in light of the recent cosmic tensions, and give a possible explanation as to why the equivalent $k$-essence models have been missed as serious competitors to $\Lambda$CDM in the past. Finally, we review the geometric foundations of the theory and show that the integrable Weyl, Schr\"{o}dinger and completely symmetric geometries are embedded within our framework as special cases.

gr-qc↗

arXiv2025

Length-preserving biconnection gravity and its cosmological implications

We consider a length-preserving biconnection gravitational theory, inspired by information geometry, which extends general relativity by using the mutual curvature as the fundamental object describing gravity. The two connections used to build up the theory are the Schrödinger connection, and its dual. It can be seen that the dual of a non-metric Schrödinger connection possesses torsion, even if the Schrödinger connection itself does not, and consequently the pair $(M,g,\nabla^{*})$ is a quasi-statistical manifold. The field equations are postulated to have the form of the standard Einstein equations, but with the Ricci tensor- and scalar replaced with the mutual curvature tensor- and scalar, resulting in additional torsion-dependent terms. The covariant divergence of the matter energy-momentum does not vanish in this theory. We derive the equation of motion for massive particles, which shows the presence of an extra force. The Newtonian limit of the equations of motion is also considered. We explore the cosmological implications by deriving the generalized Friedmann equations for the FLRW geometry. They contain additional terms that can be interpreted as describing an effective, geometric type dark energy. We examine two cosmological models: one with conserved matter, and one where dark energy and pressure are related by a linear equation of state. The predictions of both models are compared with a set of observational values of the Hubble function, and with the standard $Λ$CDM model. Length-preserving biconnection gravity models fit well the observational data, and also align with $Λ$CDM at low redshifts $(z<3)$. The obtained results suggest that a modified biconnection geometry could explain the late-time acceleration, as well as the formation of the supermassive black holes, since they predict a different age of our Universe as compared to standard cosmology.

gr-qc↗

arXiv2024

Enlargement of symmetry groups in physics: a practitioner's guide

Wigner's classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to the theory of ordinary unitary representations by enlarging the group of physical symmetries. Nevertheless, the enlargement process is not always described explicitly: it is unclear in which cases the enlargement has to be done to the universal cover, a central extension, or to a central extension of the universal cover. On the other hand, in the mathematical literature, projective unitary representations were extensively studied, and famous theorems such as the theorems of Bargmann and Cassinelli have been achieved. The present article bridges the two: we provide a precise, step-by-step guide on describing projective unitary representations as unitary representations of the enlarged group. Particular focus is paid to the difference between algebraic and topological obstructions. To build the bridge mentioned above, we present a detailed review of the difference between group cohomology and Lie group cohomology. This culminates in classifying Lie group central extensions by smooth cocycles around the identity. Finally, the take-away message is a hands-on algorithm that takes the symmetry group of a given quantum theory as input and provides the enlarged group as output. This algorithm is applied to several cases of physical interest. We also briefly outline a generalization of Bargmann's theory to time-dependent phases using Hilbert bundles.

math-ph↗

arXiv2024

Semi-Symmetric Metric Gravity: A Brief Overview

We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one, by allowing for the presence of a simple form of the torsion, described in terms of a torsion vector. The Einstein field equations are postulated to have the same form as in standard general relativity, thus relating the Einstein tensor constructed with the help of the semi-symmetric connection, with the energy-momentum tensor. The inclusion of the torsion contributions in the field equations has intriguing cosmological implications, particularly during the late-time evolution of the Universe. Presumably, these effects also dominate under high-energy conditions, and thus SSMG could potentially address unresolved issues in General Relativity and cosmology, such as the initial singularity, inflation, or the $^7$Li problem of the Big-Bang Nucleosynthesis. The explicit presence of torsion in the field equations leads to the non-conservation of the energy-momentum tensor, which can be interpreted within the irreversible thermodynamics of open systems, as describing particle creation processes. We also review in detail the cosmological applications of the theory, and investigate the statistical tests for several models, by constraining the model parameters via comparison with several observational datasets.

gr-qc↗

arXiv2024

Schrödinger Connections: From Mathematical Foundations Towards Yano-Schrödinger Cosmology

Schrödinger connections are a special class of affine connections, which despite being metric incompatible, preserve length of vectors under autoparallel transport. In the present paper, we introduce a novel coordinate-free formulation of Schrödinger connections. After recasting their basic properties in the language of differential geometry, we show that Schrödinger connections can be realized through torsion, non-metricity, or both. We then calculate the curvature tensors of Yano-Schrödinger geometry and present the first explicit example of a non-static Einstein manifold with torsion. We generalize the Raychaudhuri and Sachs equations to the Schrödinger geometry. The length-preserving property of these connections enables us to construct a Lagrangian formulation of the Sachs equation. We also obtain an equation for cosmological distances. After this geometric analysis, we build gravitational theories based on Yano-Schrödinger geometry, using both a metric and a metric-affine approach. For the latter, we introduce a novel cosmological hyperfluid that will source the Schrödinger geometry. Finally, we construct simple cosmological models within these theories and compare our results with observational data as well as the $Λ$CDM model.

gr-qc↗

arXiv2024

Semi-Symmetric Metric Gravity: from the Friedmann-Schouten geometry with torsion to dynamical dark energy models

In the present paper we introduce a geometric generalization of standard general relativity, based on a geometry initially introduced by Friedmann and Schouten in 1924, through the notion of a semi-symmetric connection. The semi-symmetric connection is a particular connection that extends the Levi-Civita one, by allowing for the presence of torsion. While the mathematical landscape of the semi-symmetric metric connections is well-explored, their physical implications remain to be investigated. After presenting in detail the differential geometric aspects of the geometries with semi-symmetric metric connection, we formulate the Einstein field equations, which contain additional terms induced by the presence of the specific form of torsion we are studying. We consider the cosmological applications of the theory by deriving the generalized Friedmann equations, which also include some supplementary terms as compared to their general relativistic counterparts and can be interpreted as a geometric type dark energy. To evaluate the proposed theory, we consider three cosmological models - the first with constant effective density and pressure, the second with the dark energy satisfying a linear equation of state, and a third one one with a polytropic equation of state. We compare the predictions of the semi-symmetric metric gravitational theory with the observational data for the Hubble function, and with the predictions of the standard $Λ$CDM model. Our findings indicate that the semi-symmetric metric cosmological models give a good description of the observational data, and for certain values of the model parameters, they can reproduce almost exactly the predictions of the $Λ$CDM paradigm. Consequently, Friedmann's initially proposed geometry emerges as a credible alternative to standard general relativity, in which dark energy has a purely geometric origin.

gr-qc↗