arXiv subjects

M. Z. Bhatti

Publications and source records attributed to M. Z. Bhatti.

At least 19 recordsLinked to original sources

arXiv2026

Physical Features of Geometrically Deformed Anisotropic Charged Three-dimensional BTZ Black Holes

This work employs the minimal geometric deformation decoupling scheme to derive interior stellar solutions in the background of an electrically charged BTZ ansatz as a seed metric in three dimensions. In this respect, we impose two different equations of state to determine the deformation function and the new material contributions emerging from the additional field source. Furthermore, we describe the finiteness of all thermodynamic quantities of the presented stellar solutions, including the effective thermodynamical quantities, for varying values of the deformation parameter and total electric charge. We explore the new interior astrophysical solutions in three-dimensional gravity by analyzing the charged BTZ metric, admitting circular symmetry through the principles of geometric deformation. This study examines the impact of radial-metric deformation on the charged BTZ geometry and underscores the importance of stellar decoupling within the context of electrically charged dense distributions. It is shown that new physically acceptable solutions by incorporating any known three-dimensional spacetime as the isotropic basis are possible, which in turn enable one to analyze the quantum effects due to low degrees of freedom at lower dimensions.

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arXiv2025

Completely Deformed Complexity-free Anisotropic Fluid Sphere

In this work, we investigate the emergence of compact, anisotropic stellar structures through the gravitational decoupling scheme within the framework of complete geometric deformation. The study introduces a novel synthesis of two independent techniques, namely the zero-complexity factor and density-like constraints, applied simultaneously to determine the deformation functions. This dual implementation represents a new methodological step in stellar modeling, as it allows us to explicitly control the role of anisotropy and complexity in the internal structure of self-gravitating objects. Starting from a chosen metric ansatz as a seed solution, we demonstrate that the zero-complexity condition captures the gravitational response of compact matter in a fully tractable form. The complete deformation procedure then yields two new physically viable anisotropic solutions, passing all standard stability and energy condition tests. Our results show, for the first time, that the direction of energy transfer between the seed sector and the decoupled source is uniquely governed by the deformation parameter, providing direct physical insight into the coupling between known and generic gravitational fields. Furthermore, we find that anisotropy plays a decisive role in the stability criteria of these stars, highlighting its nontrivial influence on realistic stellar evolution. These results offer a new perspective on the modeling of high-density stellar interiors and open a pathway for extending gravitational decoupling analyses to more complex astrophysical scenarios.

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arXiv2025

Gauss-Bonnet entropy and thermal dynamics of RN-AdS black holes

We explore the thermodynamics of a novel solution for the Reissner-Nordström-Anti-de Sitter (AdS) black hole, uniquely incorporating the Gauss-Bonnet term. Unlike previous studies that primarily focused on standard General Relativity or other modifications, this inclusion allows for a modified entropy formulation, facilitating the computation of key thermodynamic quantities such as Gibbs free energy, the first law of thermodynamics, the equation of state, and Hawking temperature. We identify critical points and graphically represent the relationship between temperature and Gibbs free energy as a function of the horizon radius. Ultimately, we assess the thermal stability of the Reissner-Nordström-AdS black hole within the framework of Gauss-Bonnet gravity, emphasizing the influence of the Gauss-Bonnet term unlike previous studies that primarily focused on standard General Relativity or other modifications. As a result, it is found that the Gauss-Bonnet coupling significantly alters the thermodynamic behavior and stability structure of the black hole, revealing richer phase transition phenomena.

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arXiv2025

Fuzzy Dark Matter Less-complex Wormhole Structures in Higher-Order Curvature Gravity

Fuzzy dark matter wormhole solutions coupled with anisotropic matter distribution are explored in higher-order curvature gravity. We derive the shape function for fuzzy wormholes and explore their possible stability. We study the embedding diagrams of the active gravitational mass associated with fuzzy dark matter wormholes by taking a certain shape function. Aiming to highlight the role of higher-order curvature gravity in the modeling of less complex fuzzy wormhole structures, we evaluate the complexity factor, the conservation equation, and null energy conditions. Our study reinforces more importance of uniformly distributed pressure effects throughout the less complex region than the emergence of energy density homogeneity in the stability of fuzzy wormholes. It is shown that the active gravitational mass of the fuzzy wormhole structures varies inversely with the radial distance, thereby suggesting the breaching of energy conditions at some arena of the Einasto index. Furthermore, it is revealed that stable fuzzy dark matter wormhole structures exist in nature in the surroundings of cold dark matter halos and galactic bulges. The important physics understood from our analysis is that in higher-order curvature gravity, feasible geometries of fuzzy dark matter wormholes exist naturally in the environments of different galactic haloes.

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arXiv2024

Role of Complexity on the Minimal Deformation of Black Holes

We investigate spherically symmetric classes of anisotropic solutions within the realm of a schematic gravitational decoupling scheme, primarily decoupling through minimal geometric deformation, applied to non-rotating, ultra-compact, self-gravitational fluid distributions. In this respect, we employ the minimal complexity factor scheme to generate physically realistic models for anisotropic matter distributions, using a well-behaved model. The zero-complexity factor condition enables us to determine the deformation function for solving the decoupled system. We explore all the structure-defining scalar variables, such as density inhomogeneity, strong energy condition, density homogeneity, and the complexity factor (an alloy of density inhomogeneity and pressure anisotropy) for the decoupling constant ranging between $0$ and $1$. We observe that the anisotropy vanishes when the coupling constant is set to unity. This finding holds significance as it implies that, in the context of a zero-complexity factor approach, an anisotropic matter distribution becomes perfect without requiring any isotropy requirements. This work effectively explored the impact of complexity on the composition of self-gravitational stellar distributions. This effective approach enables the development of new, physically realistic isotropic stellar models for anisotropic matter distributions. Additionally, our findings indicate that the complexity factor in static, spherically symmetric self-gravitational objects can significantly affect the nature of the matter distribution within these systems. It is concluded that the minimally deformed Durgapal-IV model features an increasing pressure profile, and the local anisotropy of pressure vanishes throughout the model under complexity-free conditions.

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arXiv2023

Quasi-static evolution of axially and reflection symmetric large-scale configuration

We review recently offered notions of quasi-static evolution of the axial self-gravitating structures at large-scales and the criteria to characterize the corresponding evolutionary aspects under the influence of strong curvature regimes. In doing so, we examine the axial source's dynamic and quasi-static behavior within the parameters of various modified gravity theories. We address the formalism of these notions and their possible implications in studying the dissipative and anisotropic configuration. We initiate by considering higher-order curvature gravity. The Palatini formalism of $f(R)$ gravity is also taken into consideration to analyze the behavior of the kinematical as well as the dynamical variables of the proposed problem. The set of invariant velocities is defined to comprehend the concept of quasi-static approximation that enhances the stability of the system in contrast to the dynamic mode. It is identified that vorticity and distinct versions of the structure scalars $Y_{I}$, $Y_{II}$ and $Y_{KL}$ play an important role in revealing the significant effects of a fluid's anisotropy. As another example of evolution, we check the influence of Palatini-based factors on the shearing motion of the object. A comparison-based study of the physical nature of distinct curvature factors on the propagation of the axial source is exhibited. This provides an intriguing platform to grasp the notion of quasi-static evolution together with the distinct curvature factors at the current time scenario. The importance of slowly evolving axially symmetric regimes will be addressed through the distinct modified gravitational context. Finally, we share a list of queries that, we believe, deserve to be addressed in the near future.

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arXiv2023

Gravitational decoupling of anisotropic stars in the Brans-Dicke theory

Anisotropic spherically symmetric solutions within the framework of the Brans-Dicke theory are uncovered through a unique gravitational decoupling approach involving a minimal geometric transformation. This transformation effectively divides the Einstein field equations into two separate systems, resulting in the alteration of the radial metric component. The first system encompasses the influence of the seed source, derived from the metric functions of the isotropic Tolman IV solution. Meanwhile, the anisotropic source is subjected to two specific constraints in order to address the second system. By employing matching conditions to determine the unknown constants at the boundary of the stellar object, a comprehensive examination of the internal structure of stellar systems ensues. This investigation delves into the impact of the decoupling parameter, the Brans-Dicke parameters, and a scalar field on the structural characteristics of anisotropic spherically symmetric spacetimes, all while considering the strong energy conditions.

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arXiv2023

Collapsing dynamics of relativistic fluid in modified gravity admitting a conformal Killing vector

The collapsing dynamics of relativistic fluid are explored in $f(R)$ gravity in a detailed systematic manner for the non-static spherically symmetric spacetime satisfying the equation of the conformal Killing vector. With quasi-homologous condition and diminishing complexity factor condition, exact solutions for dissipative as well as for non-dissipative systems are found and the astrophysical applications of these exact solutions are discussed. Furthermore, it is demonstrated that $f(R)=R$, which is the extensive restriction of $f(R)$ gravity, prior solutions of the collapsing fluid in general relativity, can be retrieved.

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arXiv2023

Non-Singular Bouncing Model in Energy Momentum Squared Gravity

This work is concerned to study the bouncing nature of the universe for an isotropic configuration of fluid $\mathcal{T}_{αβ}$ and Friedmann-Lemaître-Robertson-Walker metric scheme. This work is carried out under the novel $f(\mathcal{G},\mathcal{T}_{αβ} \mathcal{T}^{αβ})$ gravitation by assuming a specific model i.e, $f(\mathcal{G},\mathcal{T}^2)=\mathcal{G}+α\mathcal{G}^2+2λ\mathcal{T}^2$ with $α$ and $λ$ are constants, serving as free parameters. {The terms $\mathcal{G}$ and $\mathcal{T}^2$ served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in the gravitational action respectively, and is proportional to $\mathcal{T}^2=\mathcal{T}_{αβ} \mathcal{T}^{αβ}$.} A specific functional form of the Hubble parameter is taken to provide the evolution of cosmographic parameters. A well known equation of state parameter, $ω(t)=-\frac{k \log (t+ε)}{t}-1$ is used to represent the dynamical behavior of energy density, matter pressure and energy conditions. A detailed graphical analysis is also provided to review the bounce. Furthermore, all free parameters are set in a way, to make the supposed Hubble parameter act as the bouncing solution and ensure the viability of energy conditions. Conclusively, all necessary conditions for a bouncing model are checked.

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arXiv2023

Dynamics of self-gravitating systems in non-linearly magnetized chameleonic Brans-Dicke gravity

We study the effects of magnetic fields of non-linear electrodynamics in chameleonic Brans-Dicke theory under the existence of anisotropic spherical fluid. In particular, we explore dissipative and non-dissipative self-gravitating systems in the quasi-homologous regime with the minimal complexity constraint. As a result, under the aforementioned circumstances, several analytic solutions are found. Furthermore, by analyzing the dynamics of a dissipative fluid, it is demonstrated that a void covering the center can satisfy the Darmois criteria. The temperature of the self gravitating systems is also investigated.

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arXiv2022

Junction conditions in perfect fluid $f(\mathcal{G},~T)$ gravitational theory

This manuscript aims to establish the gravitational junction conditions(JCs) for the $f(\mathcal{G},~T)$ gravity. In this gravitational theory, $f$ is an arbitrary function of Gauss-Bonnet invariant $\mathcal{G}$ and the trace of the energy-momentum tensor $T_{μν}$ i.e., $T$. We start by introducing this gravity theory in its usual geometrical representation and posteriorly obtain a dynamically equivalent scalar-tensor demonstration on which the arbitrary dependence on the generic function $f$ in both $\mathcal G$ and $T$ is exchanged by two scalar fields and scalar potential. We then derive the JCs for matching between two different space-times across a separation hyper-surface $Σ$, assuming the matter sector to be described by an isotropic perfect fluid configuration. We take the general approach assuming the possibility of a thin-shell arising at $Σ$ between the two space-times. However, our results establish that, for the distribution formalism to be well-defined, thin-shells are not allowed to emerge in the general version of this theory. We thus obtain instead a complete set of JCs for a smooth matching at $Σ$ under the same conditions. The same results are then obtained in the scalar-tensor representation of the theory, thus emphasizing the equivalence between these two representations. Our results significantly constrain the possibility of developing models for alternative compact structures supported by thin-shells in $f(\mathcal{G},~T)$ gravity, e.g. gravastars and thin-shell wormholes, but provide a suitable framework for the search of models presenting a smooth matching at their surface, from which perfect fluid stars are possible examples.

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arXiv2022

$f(\mathcal{G},T_{αβ}T^{αβ})$ Theory and Complex Cosmological Structure

The basic objective of this investigation is to explore the impact of a novel gravitational modification, specifically, the $f(\mathcal{G}, \mathbf{T}^2)$ (where $\mathbf{T}^2 \equiv T_{αβ}T^{αβ}$, $T^{αβ}$ denotes the stress-energy tensor) model of gravitation, upon the complexity of time-dependent dissipative as well as non-dissipative spherically symmetric celestial structures. To find the complexity factor $(\mathbb{C}_{\mathbf{F}})$ from the generic version of the structural variables, we performed Herrera's scheme for the orthogonal cracking of Riemann tensor. In this endeavor, we are mainly concerned with the issue of relativistic gravitational collapse of the dynamically relativistic spheres fulfilling the presumption of minimal $\mathbb{C}_{\mathbf{F}}$. The incorporation of a less restrictive condition termed as quasi-homologous $(\mathbb{Q}_{\mathbf{H}})$ condition together with the zero $\mathbb{C}_{\mathbf{F}}$, allows us to formulate a range of exact solutions for a particular choice of $f(\mathcal{G}, \mathbf{T}^2)$ model. We find that some of the given exact solutions relax the Darmois junction conditions and describe thin shells by satisfying the Israel conditions, while some exhibit voids by fulfilling the Darmois constraints on both boundary surfaces. Eventually, few expected applications of the provided solutions in the era of modern cosmology are debated.

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arXiv2022

Quasi Static Evolution of Compact Objects in Modified Gravity

In this paper, the quasi static-approximation on the hydrodynamics of compact objects is proposed in $f(R, T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor, by exploring the axial and reflection symmetric space time stuffed with anisotropic and dissipative matter contents. The set of invariant-velocities is defined to comprehend the concept of quasi static-approximation. As a consequence, the evolution of compact objects is shown by analyzing the corresponding modified field, dynamical and scalar equations in this approximation to evoke all the feasible outcomes. Furthermore, the significance of kinematical quantities, modified heat-fluxes and scalar variables are found through the proposed approximation.

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arXiv2021

Study of Generalized Lema\^ıtre-Tolman-Bondi Spacetime in Palatini $f(R)$ Gravity

This paper aims to analyze the generalization of Lema\^ıtre-Tolman-Bondi (LTB) spacetime for dissipative dust under the influence of Palatini $f(R)$ gravity. We explore the modified field equations, kinematical variables, and mass function in this scenario. We construct Bianchi identities using conservation and differential equations for shear, expansion, and curvature scalar in the background of Palatini $f(R)$ gravity. We calculated the scalar functions coming from the orthogonal decomposition of the Riemann tensor in this framework. These scalar functions known as structure scalars have been explored for LTB spacetime using modified field equations. The symmetric properties of LTB spacetime have been discussed using two subcases. We found that generalized LTB spacetime has properties comparable with LTB and obtained structure scalars in both cases which have a similar dependence on a material profile even in Palatini gravity.

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arXiv2021

Effects of Electromagnetic Field on the Structure of Massive Compact Objects

This paper encompasses a set of stellar equations that administer the formation and evolution of self-gravitating, dissipative spherically symmetric fluid distributions having anisotropic stresses in the presence of electromagnetic field. The Riemann tensor is split orthogonally to procure five scalar functions named as structure scalars which are then utilized in the stellar equations. It is shown that some basic fluid properties such as energy density inhomogeneity, pressure anisotropy and heat flux are interlinked with the obtained scalars. Further, it is shown that all the solutions to Einstein equations can be written in terms of these five scalars keeping in view the static case.

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arXiv2021

On the Stability of Pressure Isotropy Condition in Palatini $f(R)$ Gravity

This manuscript copes with the issue of analyzing the conditions to check the stability of the pressure isotropy condition by taking into account a spherically symmetric dissipative astrophysical configuration with the Palatini $f(R)$ gravity theory. We work out a differential equation in terms of the Weyl scalar that has a crucial part in the analysis of the evolution of the considered system. Using this equation, we devise another stellar equation that characterizes the evolution of anisotropic factor. Later, we assume an axially symmetric configuration and extended our analysis for that particular symmetry. It is worth observing that the physical factors responsible for compelling an initially isotropic object to trigger pressure anisotropy incorporate energy density, dissipative flux, and shear in fluid flow.

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arXiv2021

Influence of Electromagnetic Field on Hyperbolically Symmetric Source

We pursue a coherent analysis of hyperbolically symmetric static sources by extending the work of Herrera \cite{26} to the case of electromagnetic field. We deeply analyze the impact of such a force on the physical characteristics of the hyperbolically symmetric spacetime under consideration. Setting off the Einstein's gravitational equations, we particularize the stress-energy tensor by keeping in mind the constituents of tetrad field in Minkowski coordinate system. Hyperbolically symmetric source has a vacuole in the vicinity of its center, i.e., such a distribution is unable to fill the central zone of symmetry. In all the stellar expressions, the energy density of the source comes out to be negative which demonstrates that quantum effects must be involved along with certain extreme restrictions to explicate any physical application of such a hyperbolically symmetric source. Various explicit exact solutions along with their corresponding generating functions are also worked out.

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arXiv2021

Formation of Cylindrical Gravastars in Modified Gravity

In this paper, we analyze a few physical characteristics of gravastar with cylindrical geometry in $f(R,T)$ theory, where $R$ is the Ricci scalar and $T$ is the trace of energy-momentum tensor. The gravastar is generally considered to be a substitute of a black hole with three different regions. In the present work, we examine the formulation of gravastar-like cylindrical structures in $f(R,T)$ theory. By using Darmois and Israel matching conditions, we formulate a mass function of a thin shell. We calculate the different physical characteristics of gravastar, in particular, entropy within the thin shell, proper length of the intermediate thin shell as well as energy of the shell.

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