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 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 , 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 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.,

In the present paper we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function e λ and solved the Einstein's relativistic field equations with the help of Karmarkar condition for an anisotropic matter distribution. The physical properties of our model such as pressure, density, mass function, surface red-shift, gravitational red-shift are investigated and the stability of the stellar configuration is discussed in details. Our model is free from central singularities and satisfies all energy conditions. The model we present here satisfy the static stability criterion i.e. dM/dρc > 0 for 0 ≤ ρc ≤ 4.04 × 10 17 g/cm 3 (stable region) and for ρc ≥ 4.04 × 10 17 g/cm 3 , the region is unstable i.e., dM/dρc ≤ 0.

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 +2χ T , 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 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 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 χ-coupling parameter. These predicted radii exhibit a monotonic diminishing nature as the a e-mail:

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In this article, we have presented a static anisotropic solution of stellar compact objects for selfgravitating system by using minimal geometric deformation techniques in the framework of embedding class one spacetime. For solving of this coupling system, we deform this system into two separate system through the geometric deformation of radial components for the source function λ(r) by mapping: e −λ(r) → e −λ(r) + β g(r), where g(r) is deformation function. The first system corresponds to Einstein's system which is solved by taking a particular generalized form for source functionλ(r) while another system is solved by choosing well-behaved deformation function g(r). To test the physical viability of this solution, we find complete thermodynamical observable as pressure, density, velocity, and equilibrium condition via. TOV equation etc. In addition to the above, we have also obtained the moment of inertia (I), Kepler frequency (v), compression modulus (K e) and stability for this coupling system. The M-R curve has been presented for obtaining the maximum mass and corresponding radius of the compact objects.

We present a family of new exact solutions for relativistic anisotropic stellar objects by considering a four-dimensional spacetime embedded in a five-dimensional pseudo Euclidean space, known as Class I solutions. These solutions are well behaved in all respects, satisfy all energy conditions, and the resulting compactness parameter is also within Buchdahl limit. The well-behaved nature of the solutions for a particular star solely depends on the index n. We have discussed the solutions in detail for the neutron star XTE J1739-285 (M = 1.51M , R = 10.9 km). For this particular star, the solution is well behaved in all respects for 8 ≤ n ≤ 20. However, the solutions with n < 8 possess an increasing trend of the sound speed and the solutions belonging to n > 20 disobey the causality condition. Further, the well-behaved nature of the solutions for PSR J0348+0432 (2.01M , 11 km), EXO 1785-248 (1.3M , 8.85 km), and Her X-1 (0.85M , 8.1 km) are specified by the index n with limits 24 ≤ n ≤ 54, 1.5 ≤ n ≤ 4, and 0.8 ≤ n ≤ 2.7, respectively.

We obtain a new static model of the TOV-equation for an anisotropic fluid distribution by imposing the Karmarkar condition. In order to close the system of equations we postulate an interesting form for the g rr gravitational potential which allows us to solve for g tt metric component via the Karmarkar condition. We demonstrate that the new interior solution has well-behaved physical attributes and can be utilized to model relativistic static fluid spheres. By using observational data sets for the radii and masses for compact stars such as 4U 1538-52, LMC X-4 and PSR J1614-2230 we show that our solution describes these objects to a very good degree of accuracy. The physical plausibility of the solution depends on a parameter c for a particular star. For 4U 1538-52, LMC X-4 and PSR J1614-2230 the solutions are well-behaves for 0.1574 ≤ c ≤ 0.46, 0.1235 ≤ c ≤ 0.35 and 0.05 ≤ c ≤ 0.13 respectively. The behavior of the thermodynamical and physical variables of these compact objects lead us to conclude that the parameter c plays an important role in determining the equation of state of the stellar material and observed that smaller values of c lead to stiffer equation of states.

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