The recent theoretical advance known as the minimal geometric deformation (MGD) method has initiated renewed interest in investigating higher-curvature gravitational effects in relativistic astrophysics. In this work, we model a strange star within the context of Einstein–Gauss–Bonnet gravity with the help of the MGD technique. Starting off with the Tolman metric ansatz, together with the MIT bag model equation of state applicable to hadronic matter, anisotropy is introduced via the superposition of the seed source and the decoupled energy-momentum tensor. The solution of the governing systems of equations bifurcates into two distinct models, namely, the mimicking of the θ sector to the seed radial pressure and energy density and a regular fluid model. Each of these models can be interpreted as self-gravitating static, compact objects with the exterior described by the vacuum Boulware–Deser solution. Utilizing observational data for three stellar candidates, namely PSR J1614–2230, PSR J1903+317, and LMC X-4, we subject our solutions to rigorous viability tests based on regularity and stability. We find that the Einstein–Gauss–Bonnet parameter and the decoupling constant compete against each other for ensuring physically realizable stellar structures. The novel feature of the work is the demonstration of stable compact objects with stellar masses in excess of M = 2 M _⊙ without appealing to exotic matter. The analysis contributes new insights and physical consequences concerning the development of ultracompact astrophysical entities.

In this article, we have presented a static anisotropic solution of stellar compact objects for self-gravitating system by using minimal geometric deformation techniques in the framework of embedding class one space-time. 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 $$\lambda (r)$$λ(r) by mapping: $$e^{-\lambda (r)}\rightarrow e^{-\tilde{\lambda }(r)}+\beta \,g(r)$$e-λ(r)→e-λ~(r)+βg(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 function $$\tilde{\lambda }(r)$$λ~(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 ( $$K_e$$Ke ) 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.

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.

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 behaved for \(0.1574 \le c \le 0.46\), \(0.1235 \le c \le 0.35\) and \(0.05 \le c \le 0.13\), respectively. The behavior of the thermodynamical and physical variables of these compact objects leads 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.

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, specificallyf(R, T) gravity theory. Besides, a noteworthy and achievable choice on the formulation off(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 off(R, T) as $$f(R, T)=R+2\chi T$$f(R,T)=R+2χT , whereRandTcorrespond 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. TheM–Rcurve 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 modifiedf(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.