Narrow Results

In this paper, we present new physically viable interior solutions of the Einstein field equations for static and spherically symmetric anisotropic compact stars satisfying the Karmarkar condition. For presenting the exact solutions, we provide a new suitable form of one of the metric potential functions. Obtained solutions satisfy all the physically acceptable properties of realistic fluid spheres and hence solutions are well-behaved and representing matter distributions are in equilibrium state and potentially stable by satisfying the TOV equation and the condition on stability factor, adiabatic indices. We analyze the solutions for two well-known compact stars Vela X-1 (Mass = 1.77 M${}_{\odot }$, R = 9.56 km) and Cen X-3 (Mass = 1.49 M${}_{\odot }$, R = 9.17 km).

In this paper, we searched two new exact solutions of Einstein’s field equations for modeling of compact cold stars using embedded class one spacetime continuum. We find out the expressions for pressure, density, anisotropy, redshift, metric potentials and other physical variables in terms of algebraic and trigonometric expressions and observe that all variables show well-behaved trends inside the compact stellar configurations. The causality condition is well maintained by our stellar models, i.e. the radial velocity and transverse velocity are less than l. The stability of our models is assessed via different stability criteria. The Buchdahl condition holds good for our solution. Herrera’s cracking method is applied to check the stability of stellar models. We generate anisotropic compact star models, whose masses and radii are in close agreement with the observed values for compact stars 4U 1538-52, LMCX-4, PSRJ1614-2230. A comparative analysis of the proposed models is carried out based on two different solutions reported in the paper. The appropriate graphical analysis is provided to authenticate the viability of the models.

In this paper, we employ the Karmarkar condition to model a spherically symmetric radiating star undergoing dissipative gravitational collapse within the framework of classical general relativity. The collapse ensues from an initial static core satisfying the Karmarkar condition in isotropic coordinates and proceeds nonadiabatically by emitting energy in the form of a radial heat flux to the exterior Vaidya spacetime. We show that the dynamical nature of the collapse is sensitive to the initial static configuration that inherently links the embedding to the final remnant. Our model considered several physical tests on how an initially static stellar structure onset to a radiative collapse.

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration has unequal principal stresses i.e. fluid is locally anisotropic. A certain physically motivated geometry of metric potential has been chosen and codependency of the metric potentials outlines the formation of the model. The exterior spacetime is assumed as described by the exterior Schwarzschild solution. The smooth matching of the interior to the exterior Schwarzschild spacetime metric across the boundary and the condition that radial pressure is zero across the boundary lead us to determine the model parameters. Physical requirements and stability analysis of the model demanded for a physically realistic star are satisfied. The developed model has been investigated graphically by exploring data from some of the known compact objects. The mass-radius (M-R) relationship that shows the maximum mass admissible for observed pulsars for a given surface density has also been investigated. Moreover, the physical profile of the moment of inertia (I) thus obtained from the solutions is confirmed by the Bejger–Haensel concept.

This paper explores a new embedding anisotropic charged version of a solution to Einstein–Maxwell field equations in four-dimensional spacetime through the Karmarkar conditions and the gravitational decoupling via minimal geometric decoupling (MGD) technique by choosing Pant’s interior solution [Astrophys. Space Sci. 331, 633 (2011)] as a seed solution to coupled system. Later, we integrate the coupled system within the MGD and explore a family of solutions to represent the realistic structure of nonrotating compact objects. Through the matching of the interior solutions so obtained to the exterior Reissner–Nordström metric, we tune the arbitrary constants for feasible models. After that, we subject our model to a rigorous test for a chosen parameter space to verify the physical viability of the solution for the neutron stars in EXO 1785-248 for a range of values of the decoupling constant $\sigma$. Further, we prove that the constant $\sigma$ is inherently connected to critical physical properties such as the gravitational and surface redshifts, compactification factor, mass/radius relation, etc., of the same compact star candidate EXO 1785-248. The solutions thus obtained exhibit physically viable features which are thoroughly demonstrated through graphical plots.

In this current work, we explore an anisotropic compact model with radius 9.1 km and mass 2.01 $M_{\odot }$ in the regime of Karmarkar condition in Rastall theory. To solve the extended field equations for the Rastall framework we have employed the Karmarkar condition. We investigate a comparative discussion to show the physical acceptance of Karmarkar condition in Rastall theory. Our obtained solutions, i.e. metric functions, density function and both the pressure components have well-behaved nature. The energy bounds and the equilibrium stability in the background of modified TOV equation (for Rastall proposal) are also discussed in this study. The parameter $n$ from $g_{rr}$ metric function has some important role in this current model. All the calculated properties have different natures for $n=12$ to $n=24$. In this current study we also discuss some physical parameters of this current model to check the validity of the model. In the end, it is concluded that our model is acceptable physically and geometrically.

This study is devoted to exploring the charged stellar structures under embedded space–time using the Karmarkar condition. For this, spherically symmetric space–time with the anisotropic source of fluid possessing an electric charge has been incorporated. Further, the Bardeen and Reissner–Nordstrom geometries have been employed as exterior space–time to calculate the values of the involved constants. The interior solutions of a stellar object have been worked out with the observational mass $M=2.01M_{\odot }$, and $R_{𝜖}=9.1$ km. It is argued that the acquired solutions accomplish all the necessary conditions for self-consistent charged stars. It has been noted through the detailed graphical analysis that our obtained solutions are physically stable and self-consistent with the best degree of accuracy for $n\in [12,15]$, where parameter $n$ is involved in the model under discussion. Beyond this bound $12\le n\le 15$, the realistic solutions of stellar models under discussion could not be found. After perceiving the marginal dissimilarities between our proposed models in both cases, Andreasson’s limit $\sqrt{R_{𝜖}}/3+\sqrt{R_{𝜖}/9+q^2/3R_{𝜖}}\ge \sqrt{M}$, critically important for the stellar structures, has been achieved in both the models under investigation. Lastly, it is established that the parameter $n$ has a substantial effect on worked-out solutions under the employment of Bardeen and Reissner–Nordstrom’s stellar structures.

This study is explored to discuss the anisotropic nature of charged strange compact stars by considering the MIT bag model in the context of our universe’s accelerated expansion scenario. For this purpose, we choose two models for spherically symmetric space–time components. In Model-I, we plug the embedded space–time to evaluate the Bardeen strange stellar structures. In Model-II, we choose the Krori–Barua space–time. We correlate the Bardeen geometry as an exterior solution with a spherically symmetric interior geometry to acquire unknown parameters involved in the study. We discuss the necessary properties of the strange stellar models with embedded space–time and Krori–Barua space–time via the MIT bag model. After witnessing the minor differences in our proposed models, Andreasson’s limit $\sqrt{M}\le \sqrt{R_{𝜖}}/3+\sqrt{R_{𝜖}/9+q^2/3R_{𝜖}}$ has been fulfilled as required by the charged stellar structures. Further, we conclude that all the acquired results show the stable and self-consistent behavior of charged anisotropic compact structures.

In the present paper, we discover a new well-behaved charged anisotropic solution of Einstein–Maxwell’s field equations. We ansatz the metric potential $g_{00}$ of the form given by Maurya et al. (Eur. Phys. J. C76(12) (2016) 693) with $n=2$. In their paper, it is mentioned that for $n=2$, the solution is not well-behaved for neutral configuration as the speed of sound is nondecreasing radially outward. However, the solution can represent a physically possible configuration with the inclusion of some net electric charge, i.e. the solution can become a well-behaved solution with decreasing sound speed radially outward for a charged configuration. Due to the inclusion of electric charge, the solution leads to a very stiff equation-of-state (EoS) with the velocity of sound at the center $v_{r0}^2=0.819,$$v_{t0}^2=0.923$ and the compactness parameter $u=0.823$ is close to the Buchdahl limit 0.889. This stiff EoS support a compact star configuration of mass $5.418M_{\odot }$ and radius of 10.1km.

In this paper, we generate a new generalized solution for modeling of compact anisotropic astrophysical configurations by using Karmarkar condition of embedded class 1 spacetime manifold. We demonstrate that the new solution satisfies all required physical conditions. We investigate several physical properties of compact star models, i.e. Vela X-1 (Mass $M=1.77$$M_{\odot }$, radius = $9.56$km), PSRJ $1903+327$ (Mass $M=1.667$$M_{\odot }$, radius = $9.438$km) and PSRJ $0348+0432$ (Mass $M=2.01$$M_{\odot }$, radius = $13.1$km) in conformity with the observational data. The proposed solution is free from singularities, satisfies causality condition and displays well-behaved nature inside the anisotropic configurations. All energy conditions and hydrostatic equilibrium condition are well defined inside the anisotropic fluid spheres. The adiabatic index throughout the stellar interior is greater than $4/3$ and the compactification factor lies within the Buchdahl limit $(M/R\le 4/9)$. We study the physical features of the solution in detail, analytically as well as graphically for compact star Vela X-1 with $n$ ranging from $0$ to $4.7$.

This article is based on the extension of Teleparallel Theory named $f(\tau ,T)$ gravity, where the notions $\tau$ and $T$ abbreviate the torsion trace term of the energy–momentum tensor. This study aims to explore the anisotropic outcomes of the $VelaX-1$ model. We use the field equations drawn by using the spherical symmetry, including the torsion trace term. The major components $g_{rr}$ and $g_{tt}$, of spherical symmetric space-time are obtained by inducing the Karmarkar condition. We can obtain the values of the involved parameters $c$,$P$, $Q$ in this study by matching the interior spherical metric with the exterior Schwarzschild’s solutions of the Einstein field equations. To explore the stability of the stellar objects predicted by our study, we study the properties like metric potentials, energy density, pressures, anisotropy, gradients, EoS, energy conditions, the behavior of forces, sound speeds, adiabatic index, redshift, mass function, and compactification by graphical analysis in the background of $f(\tau ,T)$ gravity.

In this study, we have explored an anisotropic stellar configuration by applying the Karmarkar condition in the framework of $F(T,{𝒯})$ [where $T$ and ${𝒯}$ stand for torsion and trace of energy–momentum tensor (EMT)] gravity. We have developed field equations of $F(T,{𝒯})$ gravity for a spherically symmetric line element and considered a viable $F(T,{𝒯})$ model, i.e. $F(T,{𝒯})=\alpha T{(r)}^2+\beta {𝒯}(r)$ (where $\alpha$ and $\beta$ are arbitrary constants) for meaningful results. Following [S. K. Maurya, B. S. Ratanpal and M. Govender, Ann. Phys.382 (2017) 36], a spherically symmetric solution of embedding class I has been explored which resulted into a generalized compact stellar model. For the evaluation of unknown parameters, we use the matching conditions at the boundary by taking spherical space-time metric as interior and Schwarzschild space-time solution as exterior space-time metric. The viability of our proposed model is checked by exploring the nature of thermodynamical variables ($\rho$, $p_r$, $p_t$), anisotropy, energy condition, Tolman–Oppenheimer–Volkov (TOV) forces, Abreu condition, equation of state parameters and adiabatic index taking the observational data of different compact stars like PSR J1416-2230, 4U 1608-52, Cen X-3, EXO 1785-248 and SMC X-1. Our stellar model is found.

In this paper, we formulate exact anisotropic interior solutions of the Einstein field equations preserving spherically symmetric geometry in the context of $f(T,{𝒯})$ gravity. To make the system close, we consider a linear function in torsion scalar $(T)$ and trace of energy–momentum tensor $({𝒯})$, and employ the well-known Karmarkar condition with metric potential of the form $e^{\lambda (r)}=1+c{r}^2{(\mathrm{\text{erf}}(1+a{r}^2))}^2$. We consider standard data of some well-known compact star models (Vela X-1, PSR J1614-2230, Cen X-3 and EXO 1785-248) to estimate the unknown model parameters. We perform physical analysis of the developed model in detail, which includes density profile, pressure profile, anisotropy factor, mass function, gravitational/surface redshift, compactness factor, energy bounds, stability criteria, and the equilibrium condition. The analysis leads us to conclude that solutions are well-behaved and physically viable.

This paper investigates the wormhole solutions in Rastall theory of gravity using the Karmarkar conditions. For this purpose, we choose a shape function (SF) that connects two asymptotically flat regions. We also discuss the wormhole configuration by plotting three-dimensional (3D) analysis of the embedding diagram in Euclidean space. Furthermore, we also observe the detailed graphical representation of energy conditions using the considered SF. The violation of energy conditions, especially null energy conditions (NEC), indicates the existence of exotic matter and wormholes. Hence, it can be concluded that our calculated results in the background of Rastall theory of gravity are viable and stable. The exciting feature of this work is the 3D analysis to discuss the viability of wormhole geometry

In this report, we present an interior solution to Einstein’s equations in a spherically symmetric and static spacetime filled by two sources with anisotropic pressures, one of these of ordinary matter for which the radial pressure is described by the MIT Bag state equation associated to the presence of quarks and the other by non-ordinary quintessence type matter. The solution is obtained from imposing the Karmarkar condition considering a metric function $g_{rr}={[1+Ca{r}^2{arctan}^2(d+a{r}^2)]}^{-1}$ resulting in a physically acceptable, stable and adequate model to represent compact objects with compactness rate $u=\frac{GM}{c^{2}R}\lesssim \frac{1}{3}$. Which allows to take different value of mass and radius in the range of the observational data of mass $M=(1.74\pm 0.14)M_{\odot }$ and radius $R=9.3\pm 1.0\mathrm{\text{km}}$ of the star 4U1608-52 with compactness $u=0.32044$, from these data we determine the range of $B_g\in [89.85,113.95]{\mathrm{\text{MeV/fm}}}^3$.

In this paper, we explore some emerging properties of the stellar objects in the frame of the $f(R,\varphi )$ gravity by employing the well-known Karmarkar condition, where $R$ and $\varphi$ represent the Ricci scalar and scalar potential, respectively. We demonstrate the embedded class-I technique by using the static spherically symmetric line element along with anisotropic fluid matter distribution. Furthermore, to achieve our goal, we take a specific expression of metric potential $g_{rr}$, already presented in the literature, and proceed by using the Karmarkar condition to obtain the second metric potential. To get the value of unknown parameters of the compact structures, we compare the Krori–Barua spacetime with spherically symmetric spacetime. Moreover, we examine the physical attributes of compact objects by presuming three viable $f(R,\varphi )$ models. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkoff equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars.