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In this work, we have obtained new phantom fluid-type traversable wormhole (WH) solutions in the context of f (R , T) modified gravity. We investigate the potential that some equations of state (EoS), specifically phantom energy, which describes the accelerated expansion of the universe, could support the existence of traversable wormholes. This cosmic fluid thus offers us a plausible explanation for the occurrence of WH geometries. We construct two WH models with matter Lagrangian density L m = - (- ρ + P r + 2 P t) and inspect numerous characteristics of these models under the WH geometry. The first WH solution (WH-I) is discovered by utilising a linear barotropic equation of state (EoS) connected with phantom energy ω < - 1 indicating the presence of the phantom fluid and pointing to the Universe's expansion, while in the second WH (WH-II) solution, we take into account an interesting EoS ρ = η (P t - P r) to generate a WH model. Additionally, it showed that the phantom fluid WH-I solution violates the radial null energy condition (NEC) while tangential NEC is satisfied. On the other hand, for the WH-II solution, NEC is violated. Extensive detailed discussions of the matter components have been done via graphical analysis. The obtained WH geometries satisfy a stable WH's physically acceptable criteria. [ABSTRACT FROM AUTHOR]

In this paper, we review a recently offered notion of quasi-static evolution of the axial self-gravitating structures at large scales and the criterium 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 the intriguing platform to grasp the notion of quasi-static evolution together with the distinct curvature factors at 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. [ABSTRACT FROM AUTHOR]

Wormholes are considered to be hypothetical tunnels connecting two distant regions of the universe or two different universes. In general relativity (GR), the formation of traversable WH requires the consideration of exotic matter that violates energy conditions (ECs). If the wormhole geometry can be described in modified gravitational theories without introducing exotic matter, it will be significant for studying these theories. In the paper, we analyze some physical properties of static traversable WH within the framework of f(R, T) modified gravitational theory. Firstly, we explore the validity of the null, weak, dominant and strong energy conditions for wormhole matter for the considered f (R , T) = R + α R 2 + λ T model. Research shows that it is possible to obtain traversable WH geometry without bring in exotic matter that violates the null energy condition (NEC) in the f(R, T) theory. The violation of the dominant energy condition (DEC) in this model may be related to quantum fluctuations or indicates the existence of special matter that violates this EC within the wormhole. Moreover, it is found that in the f (R , T) = R + α R 2 + λ T model, relative to the GR, the introduction of the geometric term α R 2 has no remarkable impact on the wormhole matter components and their properties, while the appearance of the matter-geometry coupling term λ T can resolve the question that WH matter violates the null, weak and strong energy condition in GR. Additionally, we investigate dependency of the valid NEC on model parameters and quantify the matter components within the wormhole using the "volume integral quantifier". Lastly, based on the modified Tolman–Oppenheimer–Volkov equation, we find that the traversable WH in this theory is stable. On the other hand, we use the classical reconstruction technique to derive wormhole solution in f(R, T) theory and discuss the corresponding ECs of matter. It is found that all four ECs (NEC, WEC, SEC and DEC) of matter in the traversable wormholes are valid in this reconstructed f(R, T) model, i.e we provide a wormhole solution without introducing the exotic matter and special matter in f(R, T) theory. [ABSTRACT FROM AUTHOR]

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius r + is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values r + , the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles' circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits. [ABSTRACT FROM AUTHOR]

The present article investigates the effect of f (Q) parameters on two classes of exact spherically symmetric self-bound isotropic solutions for compact objects. The field equation in f (Q) gravity is solved using Korkina–Orlyanskii and Buchdahl models. The physical validity of both models has been verified using regularity, stability, and hydrostatic equilibrium tests. We have also shown the effect of f (Q) gravity parameter α on the stability and mass–radius relation. We predicted the radii of observable compact objects GW 190814, PSR J0740+6620 PSR J1614, 2230, Cen X-3, and LMC X-4. In the absence of β , the massive neutron star GW 190814 is detected at greater values of α = 1. 5 and 1.2 for models I and II respectively. The corresponding estimated radii for both models are 15. 3 0 − 0. 29 + 0. 18 km and 15. 0 3 − 0. 25 + 0. 17 km. Additionally, as the non-metricity scalar α increases, the mass–radius decreases, and when β increases with fix α , the reverse scenario arises. Our finding indicates that a lower m a s s − g a p can be achieved in f (Q) gravity theory as compared to the standard theory of gravity. [ABSTRACT FROM AUTHOR]

James Webb Space Telescope's (JWST) observations since its launch have shown us that there could be very massive and very large galaxies, as well as massive quasars very early in the history of the Universe, conflicting expectations of the Λ CDM model. This so-called "impossibly early galaxy problem" requires too rapid star formation in the earliest galaxies than appears to be permitted by the Λ CDM model. In fact, this might not be a high masses problem, but a "time-compression problem": time too short for the observed large and massive structures to form from the initial seeds. A cosmological model that could allocate more time for the earliest large structures to form would be more conforming to the data than the Λ CDM model. In this work we are going to discuss how the recently proposed γ δ CDM model might ease and perhaps resolve the time-compression problem. In the γ δ CDM model, different energy densities contribute to the Hubble parameter with different weights. Additionally, in the formula for the Hubble parameter, energy densities depend on the redshift differently than what their physical nature dictates. This new way of relating Universe's energy content to the Hubble parameter leads to a modified relation between cosmic time and redshift. We test the observational relevance of the γ δ CDM model to the age problem by constraining its parameters with the ages of the oldest astronomical objects (OAO) together with the cosmic chronometers (CC) Hubble data and the Pantheon+ Type Ia supernovae data of the late Universe at low redshift. We find that, thanks to a modified time-redshift relation, the γ δ CDM model has a more plausible time period at high redshift for large and massive galaxies and massive quasars to form, whereas the age of the Universe today is not modified significantly. [ABSTRACT FROM AUTHOR]

In this study, we explore the traversable wormhole solutions under the framework of F (R , T) gravity with R 2 formalism such that F (R , T) = ξ R 2 + R + ζ T , where R and T represents Ricci scalar and trace of energy–momentum tensor, ζ and ξ are arbitrary constants. We consider specific form of shape functions ℧ S (r) = e 1 − r r 0 cosh (r r 0 ) and ℧ S (r) = 1 r + log r r 0 to construct traversable wormhole solutions and analyze their physical properties. Our investigation delves into the exotic matter characteristics of these wormholes, examining their matter content relative to energy conditions through comprehensive analytical and graphical analysis. Stability analysis of these configurations is conducted using the Tolman–Oppenheimer–Volkoff (TOV) equation. Additionally, we calculate the volume integral quantifier to determine the total amount of exotic matter required and analyze the active gravitational mass and complexity factor. Our findings indicate that, under specific conditions, the chosen shape functions facilitate stable and traversable wormhole solutions within the F (R , T) gravity framework. [ABSTRACT FROM AUTHOR]

In this note, a time-dependent spacetime is explored in the background of f (R , T) gravity via the gravitational collapse of a massive star. The star is modeled by the Vaidya spacetime which is time-dependent in nature. The coupling of matter with curvature is the key feature of f (R , T) theory and here we have investigated its effects on a collapsing scenario. Two different types of models, one involving minimal and the other involving nonminimal coupling between matter and curvature are considered for our study. Power law and exponential functionalities are considered as examples to check the outcome of the gravitational collapse. A detailed analysis on the appearance of horizons in Vaidya spacetime is performed and its astrophysical implications are explored. Our prime objective is to explore the nature of singularities (black hole or naked singularity) that form as an end state of the collapse. Existence of outgoing radial null geodesics from the central singularity was probed and such existence implied the formation of naked singularities thus defying the cosmic censorship hypothesis. The absence of such outgoing null geodesics would imply the formation of an event horizon and the singularity formed becomes a black hole. Conditions under which such possibilities occur are derived for all the models and sub-models. Gravitational strength of the singularity is also investigated and the conditions under which we can get a strong or a weak singularity is derived. The results obtained are very interesting and may be attributed to the coupling between curvature and matter. It is seen that for nonminimal coupling there is a possibility of a globally naked singularity, whereas for a minimal coupling scenario local nakedness is the only option. It is also found that the singularity formed can be sufficiently weak in nature, which is cosmologically desirable. [ABSTRACT FROM AUTHOR]

This paper deals with stability analysis of anisotropic-charged cylindrical geometry coupled with f (R , T) modified gravity theory (ℳ ). In this ℳ , the Lagrangian is a varying function of traces of Ricci and stress tensors. In order to examine the stable behavior of the anisotropic cylindrical cosmic object under the electromagnetic effects, we calculated the modified equations of motion and equations of continuity. in the background of f (R , T) theory. By utilizing the perturbation technique, we constitute a modified collapse equation (ℳ ℰ), which contains geometrical and physical variables in the charged scenario. Our investigation continues under the nonminimally coupled function of ℳ . Furthermore, we investigate the dynamically stable phases of charged geometry at Newtonian () and post-Newtonian (p ) epochs with the help of the rigidity parameter of fluid (Γ) by imposing some constraints on physical parameters. [ABSTRACT FROM AUTHOR]

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius r+ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values r+, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles’ circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits.

In this paper, we study the properties of electrically charged anisotropic and spherically symmetric compact stars in f (Q) gravity theory. The field equations have been solved using the MIT-Bag Equation of State (EoS) along with the Vaidya–Tikekar potential. However, the specific form of charge E 2 (r) = q 0 L 2 r 2 (1 + L r 2) 2 has been used to study the charged compact star model. The interior charge anisotropic solution has been matched with the charged Schwarzchild-(Anti)-de-Sitter metric. In particular, this study has been conducted on different compact stars viz, EXO 1785-248, PSR J1614-2230, PSR J0740+620 and SMC X-1. The mass–radius ratio of these compact stars has been predicted, and the physical viability of the model has been checked through the behaviour of causality condition, matter variables, energy constraints, modified TOV equation, and adiabatic index of the star. In conclusion, we observe a well-behaved model of a compact star in f (Q) gravity with charged matter distribution. • We have investigated charged anisotropic solutions for strange star model. • The Vaidya–Tikekar potential has been used for strange star model. • The system of equations have been solved using MIT-Bag EoS. • The obtained charged fluid solution is viable for modelling of compact objects. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of analytic wormhole solutions within the framework of f(R)$f(R)$ gravity theory. To check the possibility of having wormhole structures satisfying energy conditions, by means of the class I approach the pair {Φ(r),b(r)}$\lbrace \Phi (r), b(r)\rbrace$ describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably f(R)$f(R)$ gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the f(R)$f(R)$ gravity model and its derivatives are playing a major role, specially in considering the violation of the non–existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall–Bellman shape function, where the red–shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored. This work is devoted to the study of analytic wormhole solutions within the framework of f(R) gravity theory. To check the possibility of having wormhole structures satisfying the energy conditions, by means of the class I approach the pair {Φ(r),b(r)}$\lbrace \Phi (r), b(r)\rbrace$ describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably f(R) gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the f(R) gravity model and its derivatives are playing a major role, specially in considering the violation of the non‐existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall‐Bellman shape function, where the red‐shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of analytic wormhole solutions within the framework of f(R)$f(R)$ gravity theory. To check the possibility of having wormhole structures satisfying energy conditions, by means of the class I approach the pair {Φ(r),b(r)}$\lbrace \Phi (r), b(r)\rbrace$ describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably f(R)$f(R)$ gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the f(R)$f(R)$ gravity model and its derivatives are playing a major role, specially in considering the violation of the non–existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall–Bellman shape function, where the red–shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored. This work is devoted to the study of analytic wormhole solutions within the framework of f(R) gravity theory. To check the possibility of having wormhole structures satisfying the energy conditions, by means of the class I approach the pair {Φ(r),b(r)}$\lbrace \Phi (r), b(r)\rbrace$ describing the wormhole geometry has been obtained. Then, in conjunction with a remarkably f(R) gravity model, the satisfaction of the null and weak energy conditions at the wormhole throat and its neighborhood is investigated. To do so, some constant parameters have been bounded restricting the space parameter. In this concern, the f(R) gravity model and its derivatives are playing a major role, specially in considering the violation of the non‐existence theorem. Furthermore, the shape function should be bounded from above by the Gronwall‐Bellman shape function, where the red‐shift function plays a relevant role. By analyzing the main properties at the spatial stations and tidal accelerations at the wormhole throat, possibilities and conditions for human travel are explored. [ABSTRACT FROM AUTHOR]

We propose a new model of cosmology based on an anisotropic background and a specific f (R) theory of gravity. It is shown that field equations of f (R) gravity in a Bianchi type I background give rise to a modified Friedmann equation. This model contains two important parameters: γ and δ. We, thus, simply call our model γ δ CDM. It is distinguished in two important aspects from the Λ CDM model: firstly, the contribution of different energy densities to the Hubble parameter are weighted with different weights, and then, dependence of energy densities to redshift is modified as well. This unorthodox relation of energy content to Hubble parameter brings forth a new way of interpreting the cosmological history. This solution does not allow the existence of a cosmological constant component, however, a dark energy contribution with dependence on redshift is possible. We tested observational relevance of the new solution by best fitting to different data sets. We found that our model could accommodate the idea of cosmological coupling of black holes. [ABSTRACT FROM AUTHOR]

The paper deals with the static spherically symmetric wormhole solutions in f (R) -modified gravity theory with anisotropic matter field and for some particular choices for the shape functions. This work may be considered as an extension of the general formalism in [S. Halder, S. Bhattacharya and S. Chakraborty, Phys. Lett. B 791, 270 (2019)] for finding wormhole solutions. For isotropic matter distribution it has been shown that wormhole solutions are possible for zero tidal force and it modifies the claim in [M. Cataldo, L. Leimpi and P. Rodriguez, Phys. Lett. B 757, 130 (2016)]. Finally, energy conditions are examined and it is found that all energy conditions are satisfied in a particular domain with a particular choice of the shape function. [ABSTRACT FROM AUTHOR]

In this work we try to understand the late-time acceleration of the universe by assuming some modification in the geometry of the space and using dynamical system analysis. This technique allows to understand the behavior of the universe without analytically solving the field equations. We study the acceleration phase of the universe and stability properties of the critical points which could be compared with observational results. We consider an asymptotic behavior of two particular models f (R) = R − μ R c (R / R c) 2 n (R / R c) 2 n + 1 and f (R) = R − μ R c 1 − 1 + R 2 / R c 2 − n with n , μ , R c > 0 for the study. As a first case we fix the value of μ and analyze for all n. Later as second case, we fix the value of n and calculation are done for all μ. At the end all the calculations for the generalized case have been shown and results have been discussed in detail. [ABSTRACT FROM AUTHOR]

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models. [ABSTRACT FROM AUTHOR]

Our focus is on a specific type-N space–time that exhibits closed time-like curves in general relativity theory within the framework of Ricci-inverse gravity model. The matter-energy content is solely composed of a pure radiation field, and it adheres to the energy conditions while featuring a negative cosmological constant. One of the key findings in this investigation is the non-zero determinant of the Ricci tensor (R μ ν), which implies the existence of an anti-curvature tensor (A μ ν) and, as a consequence, an anti-curvature scalar (A ≠ R − 1 ). Furthermore, we establish that this type-N space–time serves as a solution within modified gravity theories via the Ricci-inverse model, which involves adjustments to the cosmological constant (Λ) and the energy density (ρ) of the radiation field expressed in terms of a coupling constant. As a result, our findings suggest that causality violations remain possible within the framework of this Ricci-inverse gravity model, alongside the predictions of general relativity. [ABSTRACT FROM AUTHOR]

We construct higher-dimensional and exact black holes in Einstein-Maxwell-scalar theory. The strategy we adopted is to extend the known, static and spherically symmetric black holes in the Einstein-Maxwell dilaton gravity and Einstein-Maxwell-scalar theory. Then we investigate the black hole thermodynamics. Concretely, the generalized Smarr formula and the first law of thermodynamics are derived.

We found out that gravity theory can be rewritten in the holographic language at the level of background equivalence. The examples of the bouncing cosmological models in gravity are considered in details. [ABSTRACT FROM AUTHOR]

We reconstruct gravity theory with an exponential scale factor to realize the bouncing behavior in the early universe and examine the asymptotic behavior of late-time solutions in this model. We propose an approach for the construction of asymptotic expansions of solutions of the Friedmann equations on the basis of Puiseux series. [ABSTRACT FROM AUTHOR]

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f( R, T) ( R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f( R, T)= R+2 f( T) with 'gamma-law' equation of state p = ( γ−1) ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3 β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe. [ABSTRACT FROM AUTHOR]

In this manuscript, we will examine thin-shell wormholes in the framework of f (R , T) theory. In this gravitational theory, f is a function of Ricci scalar invariant R and the trace of the stress–energy tensor T. Also, wormholes that appeared as special solutions to Einstein's field equations, are now being tackled in a variety of ways and are being viewed as viable interstellar objects. By selecting a minimally coupled f (R , T) function, we will reduce modified field equations to their corresponding Lanczos equations. The junction conditions are also manipulated and the generalized Chaplygin gas (GCG) is used to find exact solutions for traversable wormholes. We investigate the stability of these wormholes when they are perturbed while maintaining their symmetry. From the comparison of the obtained graphical solutions, it is found that only unstable solutions to thin-shell wormholes exist. • We study thin-shell wormholes in f (R , T) theory. • The junction conditions are manipulated and the generalized Chaplygin gas is used. • The stability of the wormholes is studied when they are perturbed. [ABSTRACT FROM AUTHOR]

We have shown that flat rotation curve in the framework of the generalized Newton's law of gravitation need not require dark matter. The generalized Newton's force gives rise to logarithmic potential energy at large distances from the center of the galaxy. The effect of the gravitomagnetic force is to induce the constant velocity pattern observed in flat rotation curve at very large distances from the center of the galaxy. Dynamical matter arising from moving stars far away from the center of the galaxy is shown to provide a great part to the total mass of the galaxy. [ABSTRACT FROM AUTHOR]

We find an exact spherically symmetric magnetically charged black hole solution to general relativity (GR) coupled to nonlinear electrodynamics (NED) with an appropriate Lagrangian density. In turn, starting with this spherical black hole as a seed metric, we construct a rotating spacetime, a modification of Kerr black hole, using the revised Newman–Janis algorithm that depends on mass, spin, and a NED parameter g. We find an exact expression for thermodynamic quantities of the black holes like the mass, Hawking temperature, entropy, heat capacity, and free energy expressed in terms of horizon radius, and they show significant deviations from the Kerr case owing to NED. We also calculate analytical expressions for effective Komar mass and angular momentum for the rotating black hole and demonstrate that the Komar conserved quantity corresponding to the null Killing vector at horizon obeys K χ = 2 S + T +. The radiating counterpart renders a generalization of Carmeli's spacetime as well as Vaidya's spacetime in the appropriate limits. • We report an exact spherically symmetric magnetically charged black hole solution to general relativity (GR) coupled to nonlinear electrodynamics (NED). • Further, we generalize its rotating spacetime using the revised Newman–Janis algorithm, and calculate the thermodynamic quantities, such as, the mass, Hawking temperature, entropy, heat capacity and free energy. • In the canonical ensemble, smaller magnetically charged rotating black holes ( r + < r c ) are thermodynamically preferred than the large black holes. • The Hawking–Page-type phase transition is not conceivable because the free energy is positive for all the parameter space. • Interestingly, the radiating counterpart renders a generalization of Carmeli's spacetime as well as Vaidya's spacetime in the appropriate limits. [ABSTRACT FROM AUTHOR]