The present study explores the $$f(\mathcal {R},\mathcal {T})$$f(R,T) modified gravity on the basis of observational data for three different compact stars with matter profile as anisotropic fluid without electric charge. In this respect, we adopt the well-known Karmarker condition and assume a specific and interesting model for $$\mathrm {g}_{rr}$$grr metric potential component which is compatible with this condition. This choice further leads to a viable form of metric component $$\mathrm {g}_{tt}$$gtt by utilizing the Karmarkar condition. We also present the interior geometry in the reference of Schwarzschild interior and Kohler–Chao cosmological like solutions for $$f(\mathcal {R},\mathcal {T})$$f(R,T) theory. Moreover, we calculate the spacetime constants by using the masses and radii from the observational data of three different compact stars namely 4U 1538-52, LMC X-4 and PSR J1614-2230. In order to explore the viability and stability of the obtained solutions, some physical parameters and properties are presented graphically for all three different compact object models. It is noticed that the parameters c and $$\lambda $$λ have some important and considerable role for these solutions. It is concluded that our obtained solutions are physically acceptable, bearing a well-behave nature in $$f(\mathcal {R},\mathcal {T})$$f(R,T) modified gravity.

In this paper, we discuss spherically symmetric wormhole solutions in f( R, T) modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentzian...

The present study is devoted to explore the existence of a new family of compact star solutions by adopting the Karmarkar as well as Pandey–Sharma condition in the background of $f(\mathcal{R},\mathcal{T})$ modified gravitational framework. For this purpose, we consider static spherically symmetric spacetime with anisotropic fluid distribution in absence of electric charge. In respect of Karmarkar condition, we assume a specific model of $g_{rr}$ metric potential representing a new family of solutions which is also compatible with the Pandey–Sharma condition. This assumed model permits us to calculate the $g_{tt}$ component of metric tensor by making the use of Karmarkar condition. Further, we investigate the interior solutions for $VelaX-1$ model of compact star by utilizing this new family of solutions for different values of parameter $\lambda$ . We have tuned the solution for $VelaX-1$ so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. It is found that these solutions fulfill all the necessary conditions under the observational radii and mass attribute data for small values of parameter $\lambda$ and hence physically well-behaved and promising. Through graphical analysis, it is observed that our obtained analytical solutions are physically acceptable with a best degree of accuracy for $n\in [1.8,7)-\{2,4,6\}$ , where parameter n is involved in the discussed model. It is also noticed the causality condition is violated for all $n\ge 7$ and the tangential sound velocity $v_t$ is observed as complex valued for all $0<n<1.8$ . Likewise, we explore these properties by considering large parameter $\lambda$ values. It is seen that the presented model violates all the physical conditions for $n\in \{2,4,6\}$ , while some of these for large values of $\lambda$ . Consequently, it can be concluded that the parameters n and $\lambda$ have a strong impact on the obtained solutions.

The present work is devoted to explore some interesting cosmological features of a newly proposed theory of gravity namely theory, whereRandTrepresent the Ricci scalar and trace of energy momentum‐tensor, respectively. First, a non‐equilibrium thermodynamical description is considered on the apparent horizon of the Friedmann's cosmos. The Friedmann equations are demonstrated to be equivalent to the first law of thermodynamics, i.e., , where refers to entropy production term. The constraint for validity of generalized second law of thermodynamics is also formulated and checked it for some simple well‐known forms of generic function . Next, the energy bounds for this framework and constraint the free variables by finding the validity regions for NEC and WEC are developed. Furthermore, some interesting cosmological solutions namely power law, ΛCDM, and de Sitter models in this theory are reconstructed. The reconstructed solutions are then examined by checking the validity of GSLT and energy bounds. Lastly, the stability of all reconstructed solutions by introducing suitable perturbations in the field equations is analyzed. It is concluded that obtained solutions are stable and cosmologically viable.