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In this research, we comprehensively investigate the thermodynamic properties of the Kiselev black hole and its holographic counterpart. Our investigation yields the thermodynamic product relations for the Kiselev black hole in environments permeated by dust and radiation. We establish that similar to Einstein’s gravity scenarios, the product of area (or entropy) in both contexts retains mass independence, suggesting its potential universality. In addition, we deduce bounds for the black hole’s entropy at both the inner and outer horizons. We also unveil an asymmetry between the central charges of the left and right-moving sectors when placed within the framework of universal thermodynamic principles. This asymmetry paves the way for inferring the central charges in the associated conformal field theory (CFT). Contrary to our initial findings, we observe that the central charges for the left and right-moving sectors in the CFT ultimately conform to uniform values. [ABSTRACT FROM AUTHOR]

This research paper delves into examining the Hayward black hole structure surrounded by quintessence within the framework of Finsler geometry. Our focus centers on the Finsler metric tensor development for black holes. This newly derived metric introduces significant deviations from regular black hole metrics found in general relativity due to the Finslerian term γ presence, thus shedding fresh insights into the geometry and nature of black holes. Our findings reveal that the metric structure aligns closely with known Riemannian limits, affirming the congeniality of our model with existing theories. Furthermore, we extended our analysis to derive critical mass values and determine the normalization factor for the Hayward black hole within the Finlserian framework. The study encompasses a detailed description of the horizons and extremal conditions of the Hayward black hole surrounded by quintessence and the impact of the Finsler parameter γ on them. Specifically, we explore the case where the quintessence state parameter is set to ω = - 2 / 3 . Our analysis delves into the effective potential, providing insights into null geodesics for various energy levels and examining the behavior of horizons by utilizing the definition of the effective potential. We also discuss the impact of γ for the same. We compute and analyze the radius of circular orbits, the period, the instability characteristics of circular orbits, and the force acting on photons with the newly introduced parameter γ within the quintessence field. We have thoroughly looked over the obtained results and discussed them. Additionally, we explore the shadow of the black hole in this context. Thereby, the validity and consistency of our Finslerian model are strengthened. In addition to increasing our understanding of black hole physics, this study paves the way for further research in the Finsler geometry domain and its applications in astrophysics. [ABSTRACT FROM AUTHOR]

In this article, we investigate the charged gravastar under conformal motion with the background of Finsler geometry. Mazur and Mottola pioneered the concept of the gravastar (gravitational vacuum star) for the first time. This vacuum object consists of three distinct regions, that is, (i) interior de Sitter region, (ii) thin shell consisting of ultrarelativistic stiff, and (iii) exterior vacuum Schwarzschild region. The nature of these regions can be analyzed by considering different equations of state parameters. We have studied various physical features of the gravastar, such as length, energy, entropy, stability, and the adiabatic index, both graphically and analytically within the Finslerian framework. Also, we have obtained the exact and non-singular solution for the gravastar model. [ABSTRACT FROM AUTHOR]

The intent of this article is to study the traversable wormhole (WH) models with shape function and adequate choice of redshift function in the context of Finsler geometry. The solutions obtained for the shape function of the generated wormhole satisfy the requisite metric criteria, as manifested in other investigations in the literature. By taking into account the anisotropic energy–momentum tensor, we investigate the validity of the solution of the Finsler wormhole by considering all energy conditions. We also established a wormhole solution without the need for exotic matter by considering the redshift function. Further, the result can be viewed as a graphical representation and the anisotropic factor to determine the nature of gravity of the wormhole is discussed. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to solve the Finslerian Kiselev black hole and investigate its thermodynamic characteristics surrounded by dust, radiation, quintessence, and the cosmological constant. Since these black holes have multiple horizons, thus we calculate thermodynamic quantities, including area, horizon radius, Bekenstein–Hawking entropy, Hawking temperature, surface gravity, and Komar energy products. In addition, we study all universal relations of these black holes and discuss the role and effect of the Finslerian Ricci scalar (η) on Finslerian Kiselev black holes and their stability. [ABSTRACT FROM AUTHOR]

This paper aims to study the thermodynamic features of the Reissner-Nordström-de Sitter black hole through the inner and outer horizons. We calculate different thermodynamic products such as area product, horizon radii product, Bekenstein-Hawking entropy product, Hawking temperature product, surface gravity product, Komar energy product, irreducible mass product, and specific heat product on inner and outer horizons of Reissner-Nordström-de Sitter black hole. We have found that all product formulae are dependent on black hole mass, and hence, they are not universal quantities. Furthermore, the thermodynamic stability of Reissner-Nordström-de Sitter black holes is discussed. [ABSTRACT FROM AUTHOR]

We disagree with the analysis presented in the paper entitled “Finslerian extension of an anisotropic strange star in the domain of modified gravity” (by Sourav Roy Chowdhury et al., published in Eur Phys J C 84:472, 2024). They applied the Finsler space-time to develop the Einstein field equations in the extension of modified geometry. According to the Finsler metric structure, they have considered Ric ¯ > 1 to develop a stable physical system and have also shown that the Finslerian background is a strong candidate for describing the compact system. [ABSTRACT FROM AUTHOR]

In this work, we study constant-roll inflation driven by a scalar field with the Finsler model. In this scenario, using the Hamilton–Jacobi-like formalism, an ansatz for the Hubble parameter (as a function of the scalar field), and some restrictions on the model parameters, we found new exact solutions for the inflaton potential, which include power-law, and hybrid among others. In this model, even-order slow-roll parameters approach non-negligible constants while their odd-order is asymptotically zero. [ABSTRACT FROM AUTHOR]

In this paper, we study new exact solutions of Einstein's field equations (EFEs) using 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 analyse the viability of energy conditions and also discuss the matching problem with the exterior space–time. [ABSTRACT FROM AUTHOR]

In this paper, we are going to study quintom dark energy cosmological model. In that case we introduce the action of gravity which is minimally couple to scalar field ϕ and σ with potential V (ϕ , σ) . First we write the Lagrangian of corresponding model in FRW model. Here we also introduce the non-commutative geometry and modify the above model. The deformed model leads us to obtain the equation of state. And finally we discus the present cosmological in case of phantom and quintessence. And also, we investigate the critical point and stability of system. [ABSTRACT FROM AUTHOR]