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Abstract We explore wormhole solutions sourced by Casimir energy density involving generalized uncertainty principle corrections within the framework of Rastall–Rainbow gravity. The questions of traversability and stability, as well as the presence of exotic matter, are carefully investigated. In particular, the stability issue is addressed via an approach that has not been previously employed in the context of wormholes. This method, which represents an improved version of the so-called Herrera cracking technique, has the potential to yield novel insights in the field of wormhole geometries.

Abstract The configuration of a perfect fluid distribution in an electric field under the influence of higher curvature geometric effects introduced through the Gauss–Bonnet invariants is studied in the 4 dimensional Glavan–Lin gravity formulation. It is found that whereas a constant spatially directed gravitational potential gives isothermal behaviour in the standard theory, this is not the case when extra curvature is present in general. A physically viable stellar model is constructed by assuming the Finch–Skea potential. The geometry and electrodynamics are well behaved being regular throughout the distribution including the centre. The model passes stability tests such as the Chandrasekar adiabatic stability criterion and causality. Additionally all energy conditions are satisfied within the star. We compare the performance of the model with its Einstein counterpart and observe that the higher curvature exerts a notable influence on all the physical properties of the star.

We investigate the role of a linear barotropic equation of state (p=γρ) on the structure of charged stars under higher curvature effects induced by the Gauss-Bonnet invariants in 4 dimensions. Assuming a constant spatially directed potential which gives isothermal behavior in the standard theory, the master equation is solved in terms of hypergeometric functions but a viable model could not be constructed. Setting the temporal potential to a constant, comparable to the defective Einstein static universe, interestingly admits nontrivial nonconstant exact solutions due to the higher curvature terms unlike in general relativity. Next the existence of a one-parameter group of conformal motions in the spacetime geometry was investigated. The master differential equation is solvable exactly in implicit form and explicit solutions are found for special cases. For the case of a stiff fluid p=ρ a stellar model with pleasing physical attributes is found. When the potential is assumed to vary linearly with the radius, an exact incoherent radiation model p=13ρ emerges. The physical properties of both these solutions are analyzed comprehensively with the aid of graphical plots in conjunction with suitably defined parameter spaces. It was found that both exact models passed elementary astrophysical tests for physical plausibility.

Abstract In this paper, we present new generalized wormhole (WH) solutions within the context of f(R) gravity. Specifically, we focus on f(R) gravitational theories formulated in the metric formalism, with our investigation centered on a power-law form represented by $$f(R) = \epsilon R^{\chi }$$ f ( R ) = ϵ R χ . Here, $$\epsilon $$ ϵ is an arbitrary constant, and $$\chi $$ χ is a real number. Notably, this form possesses the advantageous property of reducing to Einstein gravity when $$\epsilon =1$$ ϵ = 1 and $$\chi =1$$ χ = 1 . To obtain these novel WH solutions, we establish the general field equations for any f(R) theory within the framework of Morris–Thorne spacetime, assuming metric coefficients that are independent of time. By utilizing an anisotropic matter source and a specific type of energy density associated with solitonic quantum wave (SQW) and cold dark matter (CDM) halos, we calculate two distinct WH solutions. We thoroughly investigate the properties of the exotic matter (ExoM) residing within the WH geometry and analyze the matter contents through energy conditions (ECs). Both analytical and graphical methods are employed in this analysis to examine the validity of different regions. Notably, the calculated shape functions for the WH geometry satisfy the necessary conditions in both scenarios, emphasizing their reliability. Our investigations into specific parameter ranges in both scenarios revealed the presence of ExoM. This ExoM is characterized by an energy–momentum tensor that violates the null energy condition (NEC) and, consequently, the weak energy condition as well, in the vicinity of the WH throats. Furthermore, we investigated the repulsive effect of gravity and discovered that its presence results in a negative deflection angle for photons following null geodesics. Importantly, we observed that the deflection angle consistently exhibits negative values across all $$r_0$$ r 0 values in both scenarios, indicating the manifestation of the repulsive gravity effect. Finally, we compare the obtained WH solutions utilizing both distributions, as well as the f(R) power-law-like models, in order to assess the feasibility of energetic configurations for WHs within SQW and CDM systems.

This study presented a new exact solution for anisotropic compact stellar objects within the framework of f(R)=R+αR2 gravity. In this context, the Durgapal-Fuloria metric potential has been employed to solve the field equation derived for f(R) theory. Furthermore, we have derived the generalized Darmois-Israel junction condition necessary for seamlessly connecting the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star in the context of f(R) gravity, and the interior solution is matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These junction conditions stipulate that the pressure must not be zero at the boundary and should be proportional to the non-linear terms of f(R) gravity, a crucial aspect often overlooked by many researchers when investigating compact stellar models. Additionally, we derived the values of these parameters by using observational data of various compact stars (CSs), namely Her X-1, SAX J1808.4-3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1416-2230. This approach enables us to investigate the comprehensive analysis of solutions numerically and graphically. We conducted various physical tests, including gradient of energy density and pressures, anisotropy, stability, equilibrium conditions, energy-density constraints, mass function, compactness, redshift, and adiabatic index, to assess the feasibility of our models. Our findings demonstrate the consistent behavior of our models provides a satisfactory physical situation as far as the observational results are confirmed.

Abstract The Rastall–Rainbow gravity theory has recently been proposed as a combination of the Rastall and rainbow theories. This theory can be thought as a generalization of the Rastall gravity to an energy dependent Rastall theory, and leads to an additional degrees of freedom. In this paper, we construct models that admit the wormhole geometries within this theory. We analyze the properties of static wormholes based on the profiles of dark matter halos, which was demonstrated earlier in Rahaman et al. (Eur Phys J C 74:2750, 2014) that galactic halo possesses the necessary properties in favour of the existence of wormholes. The main properties are being analyzed by considering three different kinds of halo density profiles. Our results indicate that such wormholes could potentially exist but the NEC is violated in the vicinity of the wormhole throat. We have further examined the stability of the configuration through the adiabatic sound velocity.

The wormhole solution in dRGT massive gravity is examined in this paper in the background of non-commutative geometry. In order to derive the wormhole model, along with the zero tidal force, we assume that the matter distribution is given by the Gaussian and Lorentzian distributions. The shape function in both models involves the massive gravity parameters m2c1 and m2c2. But the spacetime loses its asymptotic flatness due to the action of the massive gravity parameter. It is noticed that the asymptotic flatness is affected by the repulsive effect induced in the massive gravitons that push the spacetime geometry very strongly. We observed that each model violates the null energy criteria, indicating the presence of exotic matter which is necessary to sustain the wormholes. The exotic matter is measured using the volume integral quantifier. Moreover, it is discovered that the model is stable under the hydrostatic equilibrium condition by utilizing the TOV equation. Finally, our research encompassed an exploration of the repulsive influence exerted by gravity. Our findings demonstrated that the presence of repulsive gravity results in a negative deflection angle for photons following null geodesics. Remarkably, we consistently observed negative values for the deflection angle across all values of r0 in the two scenarios examined. This consistent negativity unequivocally signifies the manifestation of the repulsive gravity effect.

Abstract The spherically symmetric dark energy (DE) stellar model is presented here within the context of the f(Q) theory of gravity. In order to develop the model, we take into account the linear functional form of f(Q) as $$f(Q)=mQ+n$$ f ( Q ) = m Q + n , where m is the coupling parameter and n is a real constant. We further assume that the stellar model is composed of normal baryonic matter along with DE; however, for the sake of simplicity, we avoid the interaction between them. The impact of the coupling parameter m on different physical parameters of DE stars (DESs) has been thoroughly investigated. For various values of m specified in the figure, the numerical values of the physical parameters are shown in tabular form. It is found that as m increases, the DES candidates become gradually massive and larger in size. In order to compare the behaviour of DESs with the observational results, we use the measurement of the GW190814 event and the three NS pulsars, viz. 4U1608-52 (mass $$= 1.74_{- 0.14}^{+0.14}~M_{\odot }$$ = 1 . 74 - 0.14 + 0.14 M ⊙ ), PSR J1614-2230 (mass $$=1.97_{-0.04}^{+0.04}~M_{\odot }$$ = 1 . 97 - 0.04 + 0.04 M ⊙ ), and PSR J0952-0607 (mass $$=2.35_{- 0.17}^{+0.17}~M_{\odot }$$ = 2 . 35 - 0.17 + 0.17 M ⊙ ). With the help of the $$M-R$$ M - R plot, the maximum mass of the DES obtained from our model is $$2.57~M_{\odot }$$ 2.57 M ⊙ , which is located within the lower “mass gap” range. To cover the observational constraints, this DES can be a representative for the secondary component of the GW190814 event, whose mass range is detected to be $$2.59_{-0.09}^{+0.08}~M_{\odot }$$ 2 . 59 - 0.09 + 0.08 M ⊙ by LIGO/VIRGO experiments.

Abstract This study aims to investigate spherically symmetric anisotropic solutions that describe compact stellar objects in the modified Rastall teleparallel (MRT) theory of gravity. In order to achieve this goal, we utilize the Karmarkar condition to evaluate the spherically symmetric components of the line element. We explore the field equations by selecting appropriate off-diagonal tetrad fields for two different scenarios. In the first scenario, we use a hybrid form of $$f(T)=\beta e^{m T} T^n$$ f ( T ) = β e mT T n and a linear equation of state (EoS) $$p_r=\xi \rho +\phi $$ p r = ξ ρ + ϕ , where $$0< \xi < 1$$ 0 < ξ < 1 , to evaluate h(T). In the second scenario, we again use a hybrid form of $$f(T)=\beta e^{m T} T^n$$ f ( T ) = β e mT T n and a logarithmic form of $$h(T)=\psi \log (\phi T^{\chi })$$ h ( T ) = ψ log ( ϕ T χ ) . We aim to investigate the possible forms of gravity modifications by evaluating the function for different values of m and n, reducing the gravity forms to hybrid, power law form, and exponential form. Our findings reveal that the exponential-logarithmic case is unstable in our scenario. To the best of our knowledge, we are the first to attempt to explore compact star models in MRT gravity. After obtaining the field equations, we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models. We utilize observational data, such as the mass and radius of the $$PSRJ\;1416-2230$$ P S R J 1416 - 2230 model, to ensure the physical plausibility of our findings.

Abstract This article evaluates the stability constraints of higher-dimensional geometry of thin-shell wormholes developed from the two equivalent copies of inner and outer d-dimensional charged anti-de Sitter black holes bounded by a cloud of strings and quintessence. Such geometrical structures are built using a cut-and-paste method that joins two identical forms of black hole solutions at the hypersurface. We develop the equation of motion for the constructed wormholes and then use the linear radial perturbation approach to examine the stable configuration. The stability constraints depend on the dimensions of the black holes, cloud, and quintessence parameters. It is worth mentioning that the possibility of a stable structure is greatest for the choice of d-dimensional charged anti-de Sitter black holes with quintessence and a cloud of strings.

Abstract In this paper, we introduce an anisotropic model using a dark matter (DM) density profile in Einstein–Gauss–Bonnet (EGB) gravity using a gravitational decoupling method introduced by Ovalle (Phys Rev D 95:104019, 2017), which has provided an innovative approach for obtaining solutions to the EGB field equations for the spherically symmetric structure of stellar bodies. The Tolman and Finch–Skea (TFS) solutions of two metric potentials, $$g_{tt}$$ g tt and $$g_{rr}$$ g rr , have been used to construct the seed solution. Additionally, the presence of DM in DM halos distorts spacetime, causing perturbations in the $$g_{rr}$$ g rr metric potential, where the quantity of DM is determined by the decoupling parameter $$\beta $$ β . The physical validity of the solution, along with stability and equilibrium analysis, has also been performed. Along with stability and equilibrium analysis, the solution’s physical validity has also been examined. Additionally, we have shown how both constants affect the physical characteristics of the solution. Using a $$M{-}R$$ M - R diagram, it has been described how the DM component and the GB constant affect the maximum permissible masses and their corresponding radii for various compact objects. Our model predicts the masses beyond the $$2~M_{\odot }$$ 2 M ⊙ and maximum radii $$11.92^{+0.02}_{-0.01}$$ 11 . 92 - 0.01 + 0.02 and $$12.83^{+0.01}_{-0.02}$$ 12 . 83 - 0.02 + 0.01 for larger value of $$\alpha $$ α under density order $$10^{15}~\text {g}/\text {cm}^3$$ 10 15 g / cm 3 and $$10^{14}~\text {g}/\text {cm}^3$$ 10 14 g / cm 3 , respectively, while the radii become $$11.96^{+0.01}_{-0.01}$$ 11 . 96 - 0.01 + 0.01 and $$12.81^{+0.01}_{-0.02}$$ 12 . 81 - 0.02 + 0.01 for larger value of $$\beta $$ β .

This paper develops the stellar interior geometry for charged anisotropic spherical matter distribution by developing an exact solution of the field equations of Rastall gravity using the notion of gravitational decoupling. The main purpose of this investigation is the extension of the well-known isotropic model within the context of charged isotropic Rastall gravity solutions. The second aim of this work is to apply gravitational decoupling via a minimal geometric deformation scheme in Rastall gravity. Finally, the third one is to derive an anisotropic version of the charged isotropic model previously obtained by applying gravitational decoupling technology. We construct the field equations which are divided into two sets by employing the geometric deformation in radial metric function. The first set corresponds to the seed (charged isotropic) source, while the other one relates the deformation function with an extra source. We choose a known isotropic solution for spherical matter configuration including electromagnetic effects and extend it to an anisotropic model by finding the solution of the field equations associated with a new source. We construct two anisotropic models by adopting some physical constraints on the additional source. To evaluate the unknown constants, we use the matching of interior and exterior spacetimes. We investigate the physical feasibility of the constructed charged anisotropic solutions by the graphical analysis of the metric functions, density, pressure, anisotropy parameter, energy conditions, stability criterion, mass function, compactness, and redshift parameters. For the considered choice of parameters, it is concluded that the developed solutions are physically acceptable as all the physical aspects are well-behaved.

Abstract In this work, we study the role of the vanishing complexity factor in generating self-gravitating compact objects under gravitational decoupling technique in f(Q)-gravity theory. To tackle the problem, the gravitationally decoupled action for modified f(Q) gravity has been adopted in the form $${\mathscr {S}}={{\mathscr {S}}_{Q}}+{{\mathscr {S}}^{*}_{\theta }}$$ S = S Q + S θ ∗ , where $${\mathscr {S}}_Q$$ S Q denotes the Lagrangian density of the fields which appears in the f(Q) theory while $${\mathscr {S}}^{*}_{\theta } (=\alpha {\mathscr {S}}_{\theta }$$ S θ ∗ ( = α S θ , where $$\alpha $$ α is just a coupling parameter which controls the deformation) describes the Lagrangian density for a new kind of gravitational sector which has not been included in f(Q) gravity. After that, we developed an important relation between gravitational potentials via a systematic approach (Contreras and Stuchlik in Eur Phys J C 82:706, 2022) using the vanishing complexity factor condition in the context of f(Q) theory. We have used the Buchdahl model along with the mimic-to-density constraints approach for generating the complexity-free anisotropic solution. The qualitative physical analysis has been done along with the mass-radius relation for different compact objects via $$M-R$$ M - R curves to validate our solution. It is noticed that the coupling constant $$\beta _1$$ β 1 has a definite impact on constraining the mass and radii of the object that are shown in $$M-R$$ M - R curves. The obtained results show that the compactness of the objects can be controlled by the coupling parameters.

Abstract In this article, we provide a new model of static charged anisotropic fluid sphere made of a charged perfect fluid in the context of 5D Einstein–Maxwell–Gauss–Bonnet (EMGB) gravity theory. To generate exact solutions of the EMGB field equations, we utilize the well-behaved Tolman–Kuchowicz (TK) ansatz together with a linear equation of state (EoS) of the form $$p_r=\beta \rho -\gamma $$ p r = β ρ - γ , (where $$\beta $$ β and $$\gamma $$ γ are constants). Here the exterior space-time is described by the EGB Schwarzschild metric. The Gauss–Bonnet Lagrangian term $$\mathcal {L}_{GB}$$ L GB is coupled with the Einstein–Hilbert action through the coupling constant $$\alpha $$ α . When $$\alpha \rightarrow 0$$ α → 0 , we obtain the general relativity (GR) results. Here we present the solution for the compact star candidate EXO 1785-248 with mass $$=(1.3 \pm 0.2)M_{\odot }$$ = ( 1.3 ± 0.2 ) M ⊙ ; radius $$= 10_{-1}^{+1}$$ = 10 - 1 + 1 km. respectively. We analyze the effect of this coupling constant $$\alpha $$ α on the principal characteristics of our model, such as energy density, pressure components, anisotropy factor, sound speed etc. We compare these results with corresponding GR results. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified Tolman–Oppenheimer–Volkoff (TOV) equation and the dynamical stability through the critical value of the radial adiabatic index.The mass-radius relationship is also established to determine the compactness factor and surface redshift of our model. In this way, the stellar model obtained here is found to satisfy the elementary physical requirements necessary for a physically viable stellar object.

Abstract In this paper, we attempt to construct the anisotropic solution for compact stellar configurations using the observed mass and radius of compact stars from the literature under the influence of Rastall Teleparallel gravity. To investigate the crucial elements of spherically symmetric metric space, we employed the embedding class one spacetime paradigm with Karmarkar’s condition. The field equations have been computed under the gravitational action of Rastall Teleparallel gravity. However, the unknown constants were evaluated via junction conditions using the Schwarzschild metric as the outer geometry. The compact stars analysis’s crucial physical and mathematical requirements are all admitted and shared by the model, which is physically viable and supports the emergence of novel realistic stellar configurations in Rastall Teleparallel gravity. We fix the parameters of our model to compare with three compact stars (LMC X-4, Cen X-3, and EXO 1785-248) and find that it can be regular, robust, and stable.

Abstract In this work, we attempt to find an anisotropic solution for a compact star generated by gravitational decoupling in f(Q)-gravity theory having a null complexity factor. To do this, we initially derive the complexity factor condition in f(Q) gravity theory using the definition given by Herrera (Phys Rev D 97:044010, 2018) and then derived a bridge equation between gravitational potentials by assuming complexity factor to be zero (Contreras and Stuchlik in Eur Phys J C 82:706, 2022). Next, we obtain two systems of equations using the complete geometric deformation (CGD) approach. The first system of equations is assumed to be an isotropic system in f(Q)-gravity whose isotropic condition is similar to GR while the second system is dependent on deformation functions. The solution of the first system is obtained by Buchdahl’s spacetime geometry while the governing equations for the second system are solved through the mimic constraint approach along with vanishing complexity condition. The novelty of our work is to generalize the perfect fluid solution into an anisotropic domain in f(Q)-gravity theory with zero complexity for the first time. We present the solution’s analysis to test its physical viability. We exhibit that the existence of pressure anisotropy due to gravitational within the self-gravitating bounded object plays a vital role to stabilize the f(Q) gravity system. In addition, we show that the constant involved in the solution controls the direction of energy flow between the perfect fluid and generic fluid matter distributions.

Abstract In this paper, we present an anisotropic solution for static and spherically symmetric self-gravitating systems by demanding the vanishing of the complexity factor (Herrera in Phys Rev D 97:044010, 2018) along with the isotropization technique through the gravitational decoupling (GD) approach (Ovalle in Phys Rev D 95:104019, 2017) in $$f(\mathscr {T})$$ f ( T ) -gravity theory. We begin by implementing gravitational decoupling via MGD scheme as the generating mechanism to obtain anisotropic solutions describing physically realizable static, spherical self-gravitating systems. We adopt the Krori–Barua ansatz and present two new classes of stellar solutions: the minimally deformed anisotropic solution with a vanishing complexity factor and the isotropic solution via gravitational decoupling. We demonstrate that both classes of solutions obey conditions of regularity, causality and stability. An interesting feature is the switch in trends of some of the thermodynamical quantities such as effective density, radial and transverse stresses at some finite radius, $$r=r_*$$ r = r ∗ , depending on different values of the decoupling constant $$\beta $$ β . We show that gravitational decoupling via the vanishing complexity factor enhances the stability of the stellar fluid surrounding the core’s central areas. By analyzing the effect of the decoupling constant $$\beta $$ β on the $$M-Y_{TF}$$ M - Y TF plots, (where $$Y_{TF}$$ Y TF denotes the complexity factor) derived from both solutions, we find that a small contribution from the complexity factor leads to the prediction of lower maximum mass of a self-gravitating compact star via gravitational decoupling in $$f(\mathscr {T})$$ f ( T ) -gravity compared to their pure $$f(\mathscr {T})$$ f ( T ) -gravity counterparts. Furthermore, we have also determined the impact of decoupling constant $$\beta $$ β and surface density on predicted radii via $$M{-}R$$ M - R for some known compact objects.

Abstract This paper is based on the study of compact stars in the context of electric fields and the nonmetricity effects of gravity. Due to this, we are motivated to build stellar models based on spherically symmetric space-time in f(Q) gravity. The space-time solution is obtained by Durgapal and Bannerji (Phys Rev D 27:328–331,1983) potential along with modified Van der Waals equation of state (EoS) $$p_r=\eta \rho ^2+ \frac{\beta \rho }{\gamma \rho +1}$$ p r = η ρ 2 + β ρ γ ρ + 1 by introducing a specific form of electric charge function $$q(r)=kr^3$$ q ( r ) = k r 3 . In order to validate our charge model, we used observational data from the literature for celestial objects like Her X-1, 4U 1538-52, SAX J1808.4-3658, and SMC X-1. Furthermore, we have also retrieved the uncharged effects of gravity for the model SMC X-1 by taking $$k=0$$ k = 0 . Our present physical analysis shows that all the obtained features for the present solution are in excellent agreement with the viable model as far as observational data is concerned.

Abstract A physically reasonable anisotropic stellar model is constructed with the help of the gravitational decoupling via complete geometric deformation (CGD) technique under the condition of vanishing complexity factor [Contreras and Stuchlik in Eur Phys J C 82:706 2022; Herrera, in Phys Rev D 97:044010, 2018]. The source splits into a perfect fluid and an anisotropic distribution. The Finch Skea metric proves a useful seed solution to solve the Einstein sector while the condition of vanishing complexity is invoked to solve the remaining anisotropic system of equations. A comprehensive battery of tests for physical significance is imposed on the model. Through a careful choice of parameter space, it is demonstrated that the model is regular, stable, and contains a surface of vanishing pressure establishing its boundary. Matching with the exterior metric is also achieved. Finally, the energy flows between the two sectors of the source fluid are studied graphically.

We present a rigorous study of compact objects within f ( Q ) gravity where electrical fields and dark matter are studied and provide novel mass–radius relations with models falling in the mass gap of the events GW190814 and GW200210. After formulating the basic equations and finding their relevant solutions, we impose the boundary conditions on the system under treatment. The decoupled solution for the strange stellar model with the dark matter density profile is obtained. The distribution patterns of the effective energy density and the radial as well as the tangential pressure and anisotropy in the system are intensively examined. The stability properties of the stellar configuration and the influence of dark matter are studied. The recent observations of supermassive compact star candidates such as PSR J1614–2230 and PSR J0952–0607 with observed masses greater than or equal to 2 M _⊙ have been employed in our study. Interestingly, the present study predicts the constraints on mass–radius measurements of the observed stars satisfying the equation of state based on the MIT bag model and employing the condition of mimicking, i.e., ρ ^θ = ${\chi }_{1}{\rho }_{{}_{{\rm{PI}}}}$ in f ( Q ) gravity. Our graphical results exhibit that for a particular M – R curve with fixed values of the parameters, neutron stars having mass less than M _max exist with larger radii within the context of the f ( Q ) formalism.

Abstract The purpose of this paper consists in presenting models of compact stars described by a new class of exact solutions to the field equations, in the context of general relativity, for a fluid configuration which is locally anisotropic in the pressure. With current sensitivities, we considered a non-linear form of modified Van der Waals equation of state viz., $$p_{r}=\alpha \rho ^{2} +\frac{\beta \rho }{1+\gamma \rho }$$ p r = α ρ 2 + β ρ 1 + γ ρ , as well as a gravitational potential Z(x) as a generating function by exploiting an anisotropic source of matter which served as a basis for generating the confined compact stars. The exact solutions are formed by correlating an interior space-time geometry to an exterior Schwarzschild vacuum. Then, we analyze the physical viability of the model generated and compare it with observational data of some heavy pulsars coming from the Neutron Star Interior Composition Explorer. The model satisfies all the required pivotal physical and mathematical properties in the compact structures study, offering empirical evidence in support of the evolution of realistic stellar configurations. It is shown to be regular, viable, and stable under the influence generated by the parameters coming from the theory namely, $$\alpha $$ α , $$\beta $$ β , $$\gamma $$ γ , $$\delta $$ δ , everywhere within the astral fluid in the investigated high-density regime that supports the existence of realistic heavy pulsars such as PSR J0348+0432, PSR J0740+6620 and PSR J0030+0451.

Abstract This study is devoted to explore the physical aspects of wormhole geometry under embedded class-1 spacetime in $$f(T,\tau )$$ f ( T , τ ) gravity, where $$\tau $$ τ denotes the trace of the energy-momentum tensor and T is the torsion. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. To complete this study, we take diagonal and off-diagonal tetrad, and try to build a comparison by considering the validity region of energy conditions in embedded class-1 spacetime. The embedded surface diagram is given to understand the connection between the two different regions of spacetime. The validity regions of all the energy conditions are calculated. A detailed graphical analysis is provided for validity regions of all the energy conditions. The presence of exotic matter is confirmed in both the cases as the null energy condition is violated.

Abstract In the present article, the solution of the Einstein–Maxwell field equations in the presence of a massive scalar field under the Brans-Dicke (BD) gravity is obtained via embedding approach, which describes a charged anisotropic strange star model. The interior spacetime is described by a spherically symmetric static metric of embedding class I. This reduces the problem to a single-generating function of the metric potential which is chosen by appealing to physics based on regularity at each interior point of the stellar interior. The resulting model is subjected to rigorous physical checks based on stability, causality and regularity for particular object PSR J1903+327. We also show that our solutions describe compact objects such as PSR J1903+327; Cen X-3; EXO 1785-248 and LMC X-4 to an excellent approximation. Novel results of our investigation reveal that the scalar field leads to higher surface charge densities which in turn affects the compactness and upper and lower values imposed by the modified Buchdahl limit for charged stars. Our results also show that the electric field and scalar field which originate from entirely different sources couple to alter physical characteristics such as mass-radius relation and surface redshift of compact objects. This superposition of the electric and scalar fields is enhanced by an increase in the BD coupling constant, $$\omega _{BD}$$ ω BD .

Abstract The main focus of this paper is to discuss the solutions of Einstein’s Field Equations (EFEs) for compact spherical objects study. To supply exact solution of the EFEs, we have considered the distribution of anisotropic matter governed by a new version of Chaplygin fluid equation of state (EoS). To determine different constants, we have represented the outer space-time by the Schwarzschild metric. Using the observed values of the mass for the various strange spherical object candidates, we have expanded anisotropic emphasize at the surface to forecast accurate radius estimates. Moreover, we implement various analysis to examine the physical acceptability and stability of our suggested stellar model viz., the energy conditions, cracking method, adiabatic index, etc. Graphical survey exhibits that the obtained stellar system fulfills the physical and mathematical prerequisites of the strange astrophysical object candidates Cyg X-2, Vela X-1, 4U 1636-536, 4U 1608-52, PSR J1903+327 to examine the various physical parameters and their effects on the anisotropic stellar model. The investigation reveals that complicated geometries arise from the interior matter distribution obeys a new version of Chaplygin fluid EoS and they are physically pertinent in the investigation of discovered compact structures.

Abstract The main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential $$\lambda (r)$$ λ ( r ) , and we obtained the other metric potential $$\nu (r)$$ ν ( r ) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars.

In the present paper, we focused on exploring the possibility of providing a new class of exact solutions for viable anisotropic stellar systems by means of the massive Brans–Dicke (BD) theory of gravity. In this respect, we used the decoupling of gravitational sources by minimal geometric deformation (MGD) (e−η=Ψ+βh) for compact stellar objects in the realm of embedding class-one space-time to study anisotropic solutions for matter sources through the modified Einstein field equations. For this purpose, we used the ansatz for Ψ relating to the prominent, well-known and well-behaved Finch–Skea model via Karmarkar condition, and the determination scheme for deformation function h(r) was proposed via mimic requirement on radial pressure component: θ11(r)=pr(r) and matter density: θ00(r)=ρ(r) for the anisotropic sector. Moreover, we analyzed the main physical highlights of the anisotropic celestial object by executing several physical tests for the case θ11(r)=pr(r). We have clearly shown how the parameters α, β and ωBD introduced by massive BD gravity via the MGD approach incorporating the anisotropic profile of the matter distribution have an immense effect on many physical parameters of compact bodies such as LMC X-4, LMC X-4, Her X-1, 4U 1820-30, 4U 1608-52, SAX J1808.4–658 and many others that can be fitted.

Abstract We propose a new compact stellar object model existing in a space filled with a distribution of anisotropic fluid matter for stellar configuration exposed to the hydrostatic equilibrium. An analytical solution was obtained using dark-energy (DE), which is characterized by a equation of state (EoS) of the type $$p=\gamma \rho - \rho $$ p=γρ-ρ corresponding to the external Schwarzschild vacuum solution through a thin envelope. We have imposed a collective function based on an adjustable coefficient to solve the Einstein field equations (EFEs). We investigate the general physical characteristics of high-density astrophysical objects based on the required solutions, with the inside structure of the stellar objects, such as the energy conditions, stability analysis, mass function, surface redshift function, velocity of sound and compactness of stellar objects through theoretical expression as well as graphic plots. In terms of our results, the physical behavior of this model can be used to model ultra-compact objects.

Abstract The main aim of this work is devoted to studying the existence of compact spherical systems representing anisotropic matter distributions within the scenario of alternative theories of gravitation, specifically f(R, T) gravity theory. Besides, a noteworthy and achievable choice on the formulation of f(R, T) gravity is made. To provide the complete set of field equations for the anisotropic matter distribution, it is considered that the functional form of f(R, T) as $$f(R, T)=R+2\chi T$$ f(R,T)=R+2χT , where R and T correspond to scalar curvature and trace of the stress–energy tensor, respectively. Following the embedding class one approach employing the Eisland condition to get a full space–time portrayal interior the astrophysical structure. When the space–time geometry is identified, we construct a suitable anisotropic model by using a new gravitational potential $$g_{rr}$$ grr which often yields physically motivated solutions that describe the anisotropic matter distribution interior the astrophysical system. The physical availability of the obtained model, represents the physical characteristics of the solution is affirmed by performing several physical tests. It merits referencing that with the help of the observed mass values for six compact stars, we have predicted the exact radii for different values of $$\chi $$ χ -coupling parameter. From this one can convince that the solution predicted the radii in good agreement with the observed values. Since the radius of MSP J0740+6620, the most massive neutron star observed yet is still unknown, we have predicted its radii for different values of $$\chi $$ χ -coupling parameter. These predicted radii exhibit a monotonic diminishing nature as the parameter $$\chi $$ χ going from $$-1$$ -1 to 1 gradually. The M–R curve generated from our solution can accommodate a variety of compact stars from the less massive (Her X-1) to super massive (MSP J0740+6620). So the present study uncovers that the modified f(R, T) gravity is an appropriate theory to clarify massive astrophysical systems, in any case, for $$\chi =0.0$$ χ=0.0 the standard consequences of the general relativity are recovered.

Abstract In this work, we present a new class of analytic and well-behaved solution to Einstein’s field equations describing anisotropic matter distribution. It’s achieved in the embedding class one spacetime framework using Karmarkar’s condition. We perform our analysis by proposing a new metric potential $$g_{rr}$$ grr which yields us a physically viable performance of all physical variables. The obtained model is representing the physical features of the solution in detail, analytically as well as graphically for strange star candidate SAX J1808.4-3658 ($$Mass=0.9 ~M_{\odot }$$ Mass=0.9M⊙ , $$radius=7.951$$ radius=7.951 km), with different values of parameter n ranging from 0.5 to 3.4. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, Abreu’s criterion and relativistic adiabatic index $$\varGamma $$ Γ , and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable. The physical sensitivity of the moment of inertia (I) obtained from the solutions is confirmed by the Bejger−Haensel concept, which could provide a precise tool to the matching rigidity of the state equation due to different values of n viz., $$n=0.5, 1.08, 1.66, 2.24, 2.82$$ n=0.5,1.08,1.66,2.24,2.82 and 3.4.

Abstract In the present work, we try to find a solution without singularity of Einstein’s field equations for the spherically symmetric perfect fluid objects, accurately strange quark spheres, taking into consideration Schwarzschild metric as the outside space-time. An ensemble of inside solutions found on the basis of the simplest linear state equation in the specific form $$p_r =\alpha \rho -\beta $$ pr=αρ-β . The energy density $$\rho (r)$$ ρ(r) , the radial pressure $$p_r (r)$$ pr(r) and the tangential pressure $$p_t (r)$$ pt(r) are devoid of any singularity and exhibit a well-behaved nature within the generalized anisotropic solution for compact spherical object. The generalized TOV equation is very much preserved inside the system and all energy conditions are excellent. The stability of the matter distribution of our system is checked by the concept of Herrera’s cracking and the condition of causality is all around fulfilled for our models. The adiabatic index of our specific configuration is greater than 4 / 3 in all interior points of the system and the mass-to-radius ratio in our situation is determined also lies within the Buchdahl limit i.e. $$\hbox {M}/\hbox {R}\le 4/3\,\left( {\approx 0.444} \right) $$ M/R≤4/3≈0.444 . We explore the physical characteristics based on the analytical model developed for relativistic compact stellar spheres inside the framework of the general theory of relativity. The evaluated mass and radius are in close concurrence with the observational information. We show that various physical characteristics of the known strange spherical object, viz. PSR J1614-2230, Vela X-1, 4U 1608-52, PSR J1903+327, 4U 1820-30, Cen X-3, Her X-1, and SAX J1808.4-3658, can be described by the current model.

Recent progress in the determination of both masses and radii of neutron stars has put strong constraints on the equation of state (EoS) above the nuclear saturation density. Within a confining quark matter model, we propose an anisotropic star consisting of a homogeneous and unpaired charge-neutral 3-flavor interacting quark matter with O(ms4) corrections in the context of Einstein-Gauss-Bonnet gravity theory. This generalized model depends only on three free parameters: the bag constant B, the interaction parameter a and the Gauss-Bonnet coupling constant α. Given the underlying EoS, we show the possibility of obtaining the maximal neutron star mass which satisfies the recent observational data for PSR J0751+1807. The numerical analysis of mass-radius relations supports the existence of other massive pulsars with a maximum mass consistent and common radii in the range of R≲(11∼14) Km [1]. Furthermore, we discuss the mass vs central mass density (M−ρc) relation for stability, compactness and binding energy in this gravity theory. Our results thus provide circumstantial evidence in favor of super-massive pulsars in EGB gravity.