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The Finsler-Randers space-time offers a novel perspective on cosmic dynamics, departing from the constraints of General Relativity. This paper thoroughly investigates two dark energy models resulting from the parametrization of $H$ within this geometric framework. We have conducted some geometrical and physical analysis of the dark energy models in Finslerian geometry. First, We have derived the field equations governing the universe's evolution within the Finsler-Randers formalism, incorporating the presence of dark energy. Through this, we explore its implications on cosmological phenomena, including cosmic expansion, late-time behavior of the universe, cosmological phase transition, and a few more. Also, we employ observational data such as Cosmic Chronometer, Supernovae, Gamma-Ray Bursts, Quasar, and baryon acoustic oscillations to constrain the parameters associated with dark energy in the Finsler-Randers universe. Comparing theoretical predictions with empirical observations, we assess the model viability and discern any deviations from the standard $\Lambda$CDM cosmology. Our findings offer intriguing insights into the nature of dark energy within this alternative gravitational framework, providing a deeper understanding of its role in shaping cosmic evolution. The implications of our results extend to fundamental cosmology, hinting at new avenues for research to unravel the mysteries surrounding dark energy and the geometric structure of the universe within non-standard gravitational theories., Comment: 27 pages, 32 figures

The current study explores the novel potential of traversable wormhole solutions within the framework of Finsler geometry, incorporating conformal symmetry alongside traceless fluid dynamics. Using the Conformal Killing vector approach, we have discussed the wormholes based on traceless fluid within the intriguing framework of Finsler geometry. The field equations and the associated conformal factor are obtained specifically under the condition of conformal motion in Finsler geometry. Furthermore, we have successfully derived and examined the shape function, considering a range of values for the Finslerian parameter $\lambda$. Our investigation extends to fundamental physical characteristics such as proper radial distance, active mass function, and total gravitational energy, aiming to understand their influence on the traversability of the wormhole. The observation of energy condition violations provides evidence for the exotic matter's presence near the throat, reinforcing the assertion of the Finslerian wormhole's traversability., Comment: 17 pages, 8 figures

Ricci scalar being zero is equivalent to the vacuum field equation in Finsler space-time. The Schwarzschild metric can be concluded from the field equation's solution if the space-time conserves spherical symmetry. This research aims to investigate Finslerian Schwarzschild-de Sitter space-time. Recent studies based on Finslerian space-time geometric models are becoming more prevalent because the local anisotropic structure of space-time influences the gravitational field and gives rise to modified cosmological relations. We suggest a gravitational field equation with a non-zero cosmological constant in Finslerian geometry and apprehend that the presented Finslerian gravitational field equation corresponds to the non-zero Ricci scalar. In Finsler geometry, the peer of spherical symmetry is the Finslerian sphere. Assuming space-time to conserve the "Finslerian sphere" symmetry, the counterpart of the Riemannian sphere (Finslerian sphere) must have a constant flag curvature ($\lambda$). It is demonstrated that the Finslerian covariant derivative of the geometric part of the gravitational field equation is preserved under a condition using the Chern connection. According to the string theory, string clouds can be defined as a pool of strings made due to symmetry breaking in the universe's early stages. We find that for $\lambda\neq1$, this solution resembles a black hole surrounded by a cloud of strings. Furthermore, we investigate null and time-like geodesics for $\lambda=1$. In this regard, the photon geodesics are obtained that are the closest paths to the photon sphere of the first photons visible at the black hole shadow limit. Also, circular orbit conditions are obtained for the effective potential., Comment: 30 Pages, 7 figures

This article explores wormhole solutions within the framework of Finsler geometry and the modified gravity theory. Modifications in gravitational theories, such as $f(\mathcal{R}, \mathcal{T})$ gravity, propose alternatives that potentially avoid the exotic requirements. We derive the field equations to examine the conditions for Finslerian wormhole existence and investigate geometrical and material characteristics of static wormholes using a polynomial shape function in Finslerian space-time. Furthermore, we address energy condition violations for different Finsler parameters graphically. We conclude that the proposed models, which assume a constant redshift function, satisfy the necessary geometric constraints and energy condition violations indicating the presence of exotic matter at the wormhole throat. The results are validated through analytical solutions and 3-D visualizations, contributing to the broader understanding of wormholes in Finsler-modified gravity contexts., Comment: 17 pages, 10 figures

This article investigates the properties of a wormhole model in a specific gravity theory, namely $f(Ric, T)=Ric+2\lambda T$. The wormhole solution is analyzed using an exponential shape function. The study examines various parameters, such as density, radial pressure, transverse pressure, equation-of-state parameters, and energy conditions, within the framework of deformed gravity. The research emphasizes the influence of the parameter $\lambda$ on energy condition violations and the equilibrium state of the Finslerian wormhole solution. These effects are attributed to anisotropic and hydrostatic forces present in modified gravity. The study demonstrates that the gravity model effectively captures the characteristics of wormholes within the Finslerian space-time. Additionally, the identified features of the wormhole are utilized to visualize its structure by creating a three-dimensional representation of the embedded surface. In summary, this research contributes to understanding wormholes in modified gravity theories, highlighting the importance of the parameter $\lambda$ in determining their behavior and properties., Comment: 22 pages, 18 figures

In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the Reissner-Nordstr\"{o}m-de Sitter solution. The conformal factors for static space-time structure with an elastic matter are obtained. Further, we analyze the viability of energy conditions. And also discuss the matching problem with the exterior space-time., Comment: 20 pages, 12 figures; v3 is the published version of the article

The goal of this paper is to study SdS space-time and its gravitational field with consideration of the canonical form and invariants of the curvature tensor. The characteristic of $\lambda$-tensor identifies the type of gravitational field. Gaussian curvature quantities enunciated in terms of curvature invariants., Comment: 11 pages, 6 figures

In this paper, we study the thermodynamic properties of Kiselev black hole and its holographic dual. We obtain the thermodynamic product formula for the Kiselev black hole. We consider Kiselev Black hole surrounded by both dust and radiation. We find that the area (or entropy) product formula for both cases is mass-independent as well as the case in the Einstein gravity, which interpreted as universal quantity. Moreover, we calculate the black hole entropy bound for both the inner and outer horizons. Furthermore, we show that the central charges of the left and right moving sectors are not the same via universal thermodynamic relations. Such universal relations lead us to calculate the central charge of conformal field theory (CFT). Finally, we see that the left and right of central charge of CFT are same., Comment: 17 pages, References added in the new version

In this paper we employ the Horava-Lifshitz black holes solutions and obtain the corresponding Hamiltonian. It helps us to take new variables and it will be written by harmonic oscillator form. This leads us to apply non-commutative geometry to the new Hamiltonian and obtain the corresponding Lagrangian. And then, we take some information from Finsler geometry and write the Lagrangian of the different kinds of Horava-Lifshitz black holes. We show that the corresponding Lagrangian in non-commutative and Finsler geometry for above mentioned black holes completely coincidence together with some specification of parameters. But in case of rotation, the place of center of mass energy completely different, so the particle goes to inside of black hole rapidly without falling into singularity. So in that case, two Lagrangians cover each other at $0

In this paper, we use deformation approach and obtain the corresponding Lagrangian of charged test particle. Also, we show the effect of NC parameters on the Lagrangian of test particle in HL background with charge and without charge. Also, we see in case of $\beta=\theta$ and without charge, the deformed and non-deformed Lagrangian will be same. Also in case of $\beta=\theta$ and with charge will be the same but the charge or field need some scaling. Finally, We show that two theories in case of $\beta\neq\theta$ with charge is completely different. It means that in case of NC geometry in addition to have time components of field we have $r$ and $x_{i}$ components., Comment: 9 pages

In the present work, we wanted to find the possible way in order to make the equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by investigating the massive gravity black holes. Firstly the Lagrangian of the system is introduced and then it is rewritten in the non-commutative regime by definition of the new variables. On the other hand, we focus on the Finsler geometry in order to find a Finslerian function which is equivalent to the mentioned non-commutative Lagrangian under special conditions. Also, the effective potential of the system was calculated as a part of the corresponding conditions., Comment: 13 pages

In this paper, we investigate the effects of non-commutative phase-space on the quintom cosmological model. In that case, we discuss $\Lambda_{1}$, $\Lambda_{2}$ and other cosmological parameters and show that they are associated to deformation parameters $\theta$ and $\beta$. Generally one can say that, the non-commutative parameter plays important role in physics and here also help us to arrange the divergency of cosmological constant. We draw time-dependent scale factor and investigate the effect of non-commutative parameters. Finally, we take advantage from non-commutative phase-space and obtain the deformed Lagrangian for the quintom model. In order to discuss some cosmological phenomena as dark energy and inflation, we employ Neother symmetry., Comment: 17 pages, 1 figure. References added in the revised version