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Abstract This study deals with the new class of embedded wormhole solutions in the background of general relativity. Two newly calculated wormhole solutions satisfy all the required properties. The embedded diagrams for both calculated wormhole solutions are provided. All the energy conditions are discussed through their validity regions for the different ranges of involved parameters. In maximum regions, all energy conditions are violated. We investigate the shadow and strong gravitational lensing by the wormhole throat for the two new wormhole models, namely Model-I and Model-II. The present paper considers the wormhole throat to act as a photon sphere. We first derive null geodesics using the Hamilton-Jacobi separation method to investigate the shadow and strong gravitational lensing caused by the wormhole throat. We then numerically obtain the radius of wormhole shadow, strong deflection angle, and various lensing observables by taking the example of supermassive black M87* and Sgr A* in the context of both Model-I and Model-II. Keeping all other parameters fixed, it is observed that the parameters $$\zeta _1$$ ζ 1 and $$\zeta _2$$ ζ 2 for Model-I; and $$\chi _1$$ χ 1 and $$\chi _2$$ χ 2 for Model-II have significant effects on the wormhole shadow and strong gravitational lensing phenomena. Our conclusion is that it is possible to detect relativistic images, such as Einstein rings, produced by wormholes with throat radii of $$r_{th}=3M$$ r th = 3 M . The stability analysis via Tolman–Oppenheimer–Volkov equation is included for both wormhole solutions. Additionally, current technology enables us to test hypotheses related to astrophysical wormholes.

Abstract In this paper, we investigate the phenomenon of the accelerated cosmic expansion in the late universe and the mass accretion process for a four-dimensional Einstein-Aether black hole. Starting with the basics of Einstein-Aether gravity theory, we first consider the field equations and two well-known models of Chaplygin gas, i.e., the generalized cosmic Chaplygin gas model and viscous modified Chaplygin gas model. We then obtain the energy density and Hubble parameter equations for these models in terms of various dimensionless density parameters and some unknown parameters. After finding the required parameters, we proceed with the mass accretion process. For both models, we obtain the equation of mass in terms of the redshift function and graphically represent the change in the mass of the black hole with a redshift. At the same time, we perform a graphical comparison between these models and the $$\Lambda $$ Λ CDM model of the universe. Finally, we conclude that the mass of a four-dimensional black hole will increase along the evolution of the universe within the framework of Einstein-Aether gravity.

We study the f(Q,T) gravity in the framework of Weyl geometry (known as Weyl-type f(Q,T) gravity), where Q denotes the non-metricity scalar, and T denotes the energy-momentum tensor trace. In this work, we consider the f(Q,T) model, which is defined as f(Q,T)=αQm+1+β6κ2T and investigating two scenarios: (I) m=0 (linear model) and (II) m≠0 (nonlinear model). For both scenarios, we find the explicit solution for the field equations by using the barotropic equation of state as p=wρ, where w is the equation-of-state (EoS) parameter. Further, we study the obtained solutions statistically using the Pantheon+ (Without SHOES Calibrated) dataset with 1701 data points. For both models, the best-fit values of model parameters for 1−σ and 2−σ confidence level. The higher Hubble constant values in both models emphasize the presence of Tension. We statistically compare our models to the ΛCDM model using χmin2, χred2, AIC, ΔAIC, BIC and ΔBIC. We also examine cosmological parameters such as deceleration and EoS parameters to determine the current acceleration expansion of the Universe. Furthermore, we test our model using Om diagnostic and compare it to the ΛCDM model to determine its dark energy profile. Finally, we draw the conclusion that statistically speaking, both linear and nonlinear models show good compatibility with the ΛCDM model.

Abstract We investigate the strong gravitational lensing phenomena caused by a black hole with a dark matter halo in the presence of cloud string and quintessence. This study examines strong gravitational lensing with two significant dark matter models: the universal rotation curve model and the cold dark matter model. To do this, we first numerically estimate the strong lensing coefficients and strong deflection angles for both the universal rotation curve and cold dark matter models. It is observed that the deflection angle, denoted as $$\alpha _D$$ α D , increases with the parameter $$\alpha $$ α while holding the value of $$2M \gamma $$ 2 M γ constant. Additionally, it increases with the parameter $$2M \gamma $$ 2 M γ while keeping the value of $$\alpha $$ α constant. The strong deflection angle $$\alpha _D$$ α D , for the black hole with a dark matter halo, with parameters $$\alpha $$ α and $$2\,M \gamma $$ 2 M γ , greatly enhances the gravitational bending effect and surpasses the corresponding case of the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$ A = B = 0 = α = 2 M γ ). Furthermore, we investigate the astrophysical consequences through strong gravitational lensing observations, using examples of two supermassive black holes, namely $$M87^{*}$$ M 87 ∗ and $$Sgr A^{*}$$ S g r A ∗ , located at the center of nearby galaxies. It is observed that black holes with dark matter halos in the presence of cloud string and quintessence can be quantitatively distinguished and characterized from the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$ A = B = 0 = α = 2 M γ ). The findings in our analysis suggest that observational tests for black holes influenced by dark matter halos, cloud string and quintessence are indeed feasible and viable.

Abstract The present study is based on $$f(\mathscr {T})$$ f ( T ) gravity, where we impose possible observational constraints on the model parameters to obtain physically plausible features of compact stars, specifically neutron stars. To do so, as a first step, we consider the field equations in the $$f(\mathscr {T})$$ f ( T ) gravity framework. We then solve the field equations to generate a set of new exact solutions in $$f(\mathscr {T})$$ f ( T ) gravity where model parameters are found by using boundary conditions. A few tests are performed to asses the stability of the model and compare the obtained results with observations of compact stars, in particular with the compact binary merger event GW190814. We observe the maximum mass of the star beyond the $$3M_{\odot }$$ 3 M ⊙ when the surface density is of the order $$10^{14}$$ 10 14 gm/cm $$^3$$ 3 for the higher torsion parameter, which implies that an anisotropic solution in teleparallel gravity is more suitable for modeling of massive compact objects in lower $$mass-gap$$ m a s s - g a p , and thus the model presented herein provides a satisfactory physical scenario with respect to the observational signature.

Abstract We investigate strong gravitational lensing by quantum-improved charged black holes characterized by an additional parameter denoted as $$\omega $$ ω , in addition to the mass M and charge Q. Our findings reveal that when both the parameters Q/2M and $$\omega /4M^2$$ ω / 4 M 2 increase simultaneously, various astrophysical consequences, such as the deflection angle $$\alpha _D(u)$$ α D ( u ) and angular image separation increase. Concurrently, the angular position $$\theta _{\infty }$$ θ ∞ , relative magnification $$r_{mag}$$ r mag , and the time delay $$\Delta T_{2,1}$$ Δ T 2 , 1 between the first and second relativistic images also decrease with the growing values of the parameters Q/2M and $$\omega /4M^2$$ ω / 4 M 2 . It is also observed that the Einstein ring $$\theta _1^E$$ θ 1 E for the quantum-improved charged black hole is more significant than those for Schwarzschild, quantum-improved Schwarzschild, and Reisner–Nordström black holes. As with supermassive black holes such as $$M87^*$$ M 87 ∗ and $$SgrA^*$$ S g r A ∗ , it is observed that to be a viable astrophysical black hole, the EHT results constrain the parameter space ( $$\omega /4M^2$$ ω / 4 M 2 , Q/2M). Remarkably, the EHT results for $$SgrA^*$$ S g r A ∗ impose more stringent limits on the parameter space of quantum-improved charged black holes compared to those established by the EHT results for $$M87^*$$ M 87 ∗ . We investigate the radial profiles of orbital and radial harmonic oscillation frequencies as a function of the dimensionless coupling constants and black hole mass. The main characteristics of test particle quasi-periodic oscillations close to stable circular orbits in the black hole equatorial plane are also examined. We study the positioning of resonant radii in the background of quantum-improved charged black holes for high-frequency quasi-periodic oscillations models: warped disc (WD) models, relativistic precession (RP) and its types, and epicyclic resonance (ER) and its variants.

Abstract In this work, we assume that the FLRW universe, which is filled with dark matter along with dark energy, is in the framework of Hořava–Lifshitz (HL) gravity. The dark energy is considered as the linear (Model I) and CPL (Model II) parameterizations of the equation of state parameter. For both models, we express the Hubble parameter H(z) in terms of the model parameters and redshift z. To rigorously constrain the model, we have employed a comprehensive set of recent observational datasets, including cosmic chronometers (CC), type Ia supernovae (SNIa), baryon acoustic oscillations (BAO), gamma-ray burst (GRB), quasar (Q) and cosmic microwave background radiation (CMB). Through the joint analysis of this diverse collection of datasets, we have achieved tighter constraints on the model’s parameters. This, in turn, allows us to delve into both the physical and geometric aspects of the model with greater precision. Furthermore, our analysis has enabled us to determine the present values of crucial cosmological parameters, including $$H_{0}$$ H 0 , $$\Omega _{m0}$$ Ω m 0 , $$\Omega _{k0}$$ Ω k 0 and $$\Omega _{\Lambda 0}$$ Ω Λ 0 . It is noteworthy that our results are consistent with recent findings from Planck 2018, underscoring the reliability and relevance of our models in the current cosmological context. We also conduct analysis of cosmographic parameters and apply statefinder and diagnostic tests to explore the evolution of the Universe. In addition, the statistical analysis suggests that the $$\Lambda $$ Λ CDM model is the preferred model among all our considered models. Our investigation into the models has unveiled intriguing features of the late Universe.

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 7Li 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.

Abstract Tuning the electronic properties of transition metals using pyrophosphate (P2O7) ligand moieties can be a promising approach to improving the electrochemical performance of water electrolyzers and supercapacitors, although such a material’s configuration is rarely exposed. Herein, we grow NiP2O7, CoP2O7, and FeP2O7 nanoparticles on conductive Ni-foam using a hydrothermal procedure. The results indicated that, among all the prepared samples, FeP2O7 exhibited outstanding oxygen evolution reaction and hydrogen evolution reaction with the least overpotential of 220 and 241 mV to draw a current density of 10 mA/cm2. Theoretical studies indicate that the optimal electronic coupling of the Fe site with pyrophosphate enhances the overall electronic properties of FeP2O7, thereby enhancing its electrochemical performance in water splitting. Further investigation of these materials found that NiP2O7 had the highest specific capacitance and remarkable cycle stability due to its high crystallinity as compared to FeP2O7, having a higher percentage composition of Ni on the Ni-foam, which allows more Ni to convert into its oxidation states and come back to its original oxidation state during supercapacitor testing. This work shows how to use pyrophosphate moieties to fabricate non-noble metal-based electrode materials to achieve good performance in electrocatalytic splitting water and supercapacitors.

Abstract The current manuscript deals with the tidal force effects, geodesic deviation, and shadow constraints of the Schwarzschild-like black hole theorised in Starobinsky–Bel-Robinson gravity exhibiting M-theory compactification. In the current analysis, we explore the radial and angular tidal force effects on a radially in-falling particle by the central black hole, which is located in this spacetime. We also numerically solve the geodesic deviation equation and study the variation of the geodesic separation vector with the radial coordinate for two nearby geodesics using suitable initial conditions. All the obtained results are tested for Sag A* and M87* by constraining the value of the stringy gravity parameter $$\beta $$ β using the shadow data from the event horizon telescope observations. All the results are compared with Schwarzschild black hole spacetime. In our study, we found that both the radial and angular tidal forces experienced by a particle switch their initial behaviour and turn compressive and stretching, respectively, before reaching the event horizon. The geodesic deviation shows an oscillating trend as well for the chosen initial condition. For the constrained value of $$\beta $$ β , we see that the spacetime geometry generated by Sag A* and M87* is effectively same for both Schwarzschild and Starobinsky–Bel-Robinson black hole. Furthermore, we also calculated the angular diameter of the shadow in Starobinsky–Bel-Robinson black hole and compared with the Schwarzschild black hole. It is observed that the angular diameter of shadow for M87* and Sgr A* in Starobinsky–Bel-Robinson black hole is smaller than the Schwarzschild black hole. The calculated results satisfy the event horizon telescope observational constraints.

Abstract The paper is devoted to study the observational signatures of $$f(R,G,\mathcal {T})$$ f ( R , G , T ) gravity in FRW universe. In this research article, we present a new cosmological model formulated within the $$f(R,G,\mathcal {T})$$ f ( R , G , T ) framework. To constrain the model parameters, we employ the Markov Chain Monte Carlo (MCMC) technique, which enables us to explore the parameter space effectively, and used the 36 points of cosmic chronometers and 1701 points from Pantheon Plus data. We compare our proposed $$f(R,G,\mathcal {T})$$ f ( R , G , T ) model with the widely accepted $$\Lambda $$ Λ CDM model, considering different cosmological parameters, including deceleration, snap, and jerk. By evaluating these parameters, we gain valuable insights into the dynamics and evolution of the universe within the context of our new model. Moreover, various diagnostic tests have been conducted, such as Statefinder and Om diagnostic, to further investigate the behavior and consistency of our $$f(R,G,\mathcal {T})$$ f ( R , G , T ) model. These tests offer deeper insights into the properties of our model and its compatibility with observational data. We subject our model to statistical analysis using Information Criteria, which serves as a rigorous quantitative assessment of the model’s goodness of fit to the data. This analysis aids in determining the level of agreement between our $$f(R,G,\mathcal {T})$$ f ( R , G , T ) model and the observational data, thus establishing the viability and reliability of our proposed cosmological framework. Our findings highlight the potential of the $$f(R,G,\mathcal {T})$$ f ( R , G , T ) framework in understanding the fundamental aspects of the universe’s evolution and dynamics. The comparative analysis with $$\Lambda $$ Λ CDM, as well as the comprehensive diagnostic tests performed, demonstrate the efficacy and validity of our model in explaining the observed cosmological phenomena. These results contribute to the ongoing pursuit of accurate and comprehensive models that can provide a deeper understanding of the nature of our universe.

Abstract We further investigate the dark energy model based on the Finsler geometry inspired osculating Barthel–Kropina cosmology. The Barthel–Kropina cosmological approach is based on the introduction of a Barthel connection in an osculating Finsler geometry, with the connection having the property that it is the Levi-Civita connection of a Riemannian metric. From the generalized Friedmann equations of the Barthel–Kropina model, obtained by assuming that the background Riemannian metric is of the Friedmann–Lemaitre–Robertson–Walker type, an effective geometric dark energy component can be generated, with the effective, geometric type pressure, satisfying a linear barotropic type equation of state. The cosmological tests, and comparisons with observational data of this dark energy model are considered in detail. To constrain the Barthel–Kropina model parameters, and the parameter of the equation of state, we use 57 Hubble data points, and the Pantheon Supernovae Type Ia data sample. The st statistical analysis is performed by using Markov Chain Monte Carlo (MCMC) simulations. A detailed comparison with the standard $$\Lambda $$ Λ CDM model is also performed, with the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) used as the two model selection tools. The statefinder diagnostics consisting of jerk and snap parameters, and the Om(z) diagnostics are also considered for the comparative study of the Barthel–Kropina and $$\Lambda $$ Λ CDM cosmologies. Our results indicate that the Barthel–Kropina dark energy model gives a good description of the observational data, and thus it can be considered a viable alternative of the $$\Lambda $$ Λ CDM model.

Background/Objective: Human walking involves the coordination of brain, nerves, and muscles. A disturbance in their coordination may result in gait disorder. The gait disorder may be treated through manually assisted gait training or with the aid of assistive devices/robotic devices. These robotic devices involve mechanisms which are synthesized using complex conventional procedures. Therefore, in this study, a new gait-based synthesis procedure is proposed, which simplifies the mechanism synthesis and helps to develop a mechanism which can be used in rehabilitation devices, bipeds, etc. Methods: This article presents a novel procedure for the synthesis of 4-bar linkage using the natural gait trajectories. As opposed to the conventional synthesis procedures, in this procedure, a global reference frame is considered, which allows the use of hip trajectory while moving. Moreover, this method is divided into two stages, and five precision points are considered on the hip trajectory in each stage. In the first stage, the 4-bar linkage is designed, thereafter, the configurations of the linkage for the remaining precision points are determined in the second stage. The proposed synthesis procedure reduces the complexity involved in the synthesis and helps in the simplification of the problem formulation. A two-stage optimization problem is formulated for minimizing the error between the generated and desired hip trajectories. Two nature-inspired algorithms are used for solving the optimization problem. The obtained best results are presented, and the designed linkage is simulated in MATLAB. Results: The best design of the linkage is obtained using particle swarm optimization. The trajectories generated by the designed linkage using the proposed methodology can accurately track the desired path, which indicates that designed linkage can achieve all the orientations required during walking. The positions of a whole lower limb at all the desired precision points are demonstrated by stick diagram for one gait. Conclusion: The proposed methodology has reduced the complexity of synthesis procedures and used optimization techniques to obtain a feasible design of the mechanism. The stick diagram of the designed mechanism obtained using the proposed method indicates that the designed mechanism can walk smoothly. Hence, the designed mechanism can be used in the rehabilitation devices. Furthermore, a conceptual design of an exoskeleton knee is also presented. The Translational Potential of this Article: Many hospitals and individuals have used the immobile and portable rehabilitation devices. These devices involve mechanisms, and the design of mechanism plays a vital role in the functioning of these devices; therefore, we have developed a new synthesis procedure for the design of the mechanism. Besides synthesis procedure, a mechanism is developed that can be used in the rehabilitation devices, bipeds, exoskeletons, etc., to benefit the society.

A classical solution where the (scalar) field value moves by an ${\cal O}(1)$ range in Planck units is believed to signal the breakdown of Effective Field Theory (EFT). One heuristic argument for this is that such a field will have enough energy to be inside its own Schwarzschild radius, and will result in collapse. In this paper, we consider an inverse problem: what kind of field ranges arise during the gravitational collapse of a classical field? Despite the fact that collapse has been studied for almost a hundred years, most of the discussion is phrased in terms of fluid stress tensors, and not fields. An exception is the scalar collapse made famous by Choptuik. We re-consider Choptuik-like systems, but with the emphasis now on the evolution of the scalar. We give strong evidence that generic spherically symmetric collapse of a massless scalar field leads to super-Planckian field movement. But we also note that in every such supercritical collapse scenario, the large field range is hidden behind an apparent horizon. We also discuss how the familiar perfect fluid models for collapse like Oppenheimer-Snyder and Vaidya should be viewed in light of our results.