In the present paper we obtain an anisotropic analog of the Durgapal and Fuloria (Gen Relativ Gravit 17:671, 1985 ) perfect fluid solution. The methodology consists of contraction of the anisotropic factor \(\Delta \) with the help of both metric potentials \(e^{\nu }\) and \(e^{\lambda }\). Here we consider \(e^{\lambda }\) the same as Durgapal and Fuloria (Gen Relativ Gravit 17:671, 1985 ) did, whereas \(e^{\nu }\) is as given by Lake (Phys Rev D 67:104015, 2003 ). The field equations are solved by the change of dependent variable method. The solutions set mathematically thus obtained are compared with the physical properties of some of the compact stars, strange star as well as white dwarf. It is observed that all the expected physical features are available related to the stellar fluid distribution, which clearly indicates the validity of the model.

The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically $f(R,\mathcal{T}$) gravity theory. Additionally, we have taken $f(R,\mathcal{T})$ as a linear function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as $f(R,\mathcal{T})=R+2\chi \mathcal{T}$, where $\chi$ is a dimensionless coupling parameter, and the Lagrangian matter ${\mathcal{L}}_m=-\frac{1}{3}(2p_t+p_r)$, to describe the complete set of field equations for the anisotropic matter distribution. We follow the embedding class I procedure using the Eisland condition to obtain a full space-time description inside the stellar configuration. Once the space-time geometry is specified, we determine the complete solution of modified Einstein equations by using the MIT bag model equation of state $p_r=\frac{1}{3}(\rho -4B)$ that describes the strange quark matter (SQM) distribution inside the stellar system, where $B$ denotes a bag constant. The physical validity of our anisotropic solution is confirmed by executing several physical tests. It is worth mentioning that with the help of the observed mass values for the various strange star candidates, we have predicted the exact radii by taking different values for $\chi$ and $B$. These predicted radii show a monotonic decreasing nature as the parameter $\chi$ is moved from $-0.8$ to 0.8 progressively. In this case, our anisotropic stellar system becomes more massive and transforms into more dense compact stars. We also perform a detailed graphical analysis of the compact star. As a result, for $\chi <0$, the current modified $f(R,\mathcal{T})$ gravity seems promising to explain the observed massive compact astrophysical objects, similar to magnetars, massive pulsars, and Chandrasekhar super white dwarfs, which are not justified in the framework of general relativity. Finally, we note that when $\chi =0$, general relativity results for anisotropic matter distributions are recovered.

In this article we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized metric potential, namely, Buchdahl ansatz [Phys. Rev. D 116, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar and Finch-Skea. We developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that has a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter $K$ and analyzed them in a uniform manner. As a result it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the frame work of anisotropic hypothesis, we consider analogue objects with similar mass and radii, such as LMC X-4, SMC X-1, EXO 1785-248 etc. to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of $P=P(\rho )$, we demonstrate that equation of state (EoS) can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [ Phys. Rev. D 67, 104015 (2003)]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this model, such as the energy conditions, speeds of sound, and compactness of the star, in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

We study a specific model of anisotropic strange stars in the modified $f\left(R,\mathcal {T}\right)$-type gravity by deriving solutions to the modified Einstein field equations representing a spherically symmetric anisotropic stellar object. We take a standard assumption that $f(R,\mathcal {T})=R+2\chi \mathcal {T}$, where R is Ricci scalar, $\mathcal {T}$ is the trace of the energy–momentum tensor of matter, and χ is a coupling constant. To obtain our solution to the modified Einstein equations, we successfully apply the ‘embedding class one’ techniques. We also consider the case when the strange quark matter (SQM) distribution is governed by the simplified MIT bag model equation of state given by $p_r=\frac{1}{3}\left(\rho -4B\right)$, where B is bag constant. We calculate the radius of the strange star candidates by directly solving the modified TOV equation with the observed values of the mass and some parametric values of B and χ. The physical acceptability of our solutions is verified by performing several physical tests. Interestingly, besides the SQM, another type of matter distribution originates due to the effect of coupling between the matter and curvature terms in the $f\left(R,\mathcal {T}\right)$ gravity theory. Our study shows that with decreasing the value of χ, the stellar systems under investigations become gradually massive and larger in size, turning them into less dense compact objects. It also reveals that for χ < 0 the $f\left(R,\mathcal {T}\right)$ gravity emerges as a suitable theory for explaining the observed massive stellar objects like massive pulsars, super-Chandrasekhar stars, and magnetars, etc., which remain obscure in the standard framework of General Relativity.