Modeling of compact stars: an anisotropic approach

We present here a new class of singularity free interior solutions relevant for the description of realistic anisotropic compact stellar objects with spherically symmetric matter distribution. In this geometric approach, specific choices of one of the metric functions and a selective anisotropic profile allow us to develop a stellar model by solving Einstein Field equations. The interior solutions thus obtained are matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These matching conditions together with the condition that the radial pressure vanishes at the boundary are used to fix the model parameters. The different physical features for the developed model explicitly studied from the aspect of the pulsar 4U $$1820-30$$ with its current estimated data (mass $$=1.46 \pm 0.21~M\odot $$ and radius $$=11.1 \pm 1.8$$  km (Ozel et al.: ApJ 820(1): 28, 2016) ). Analysis has shown that all the physical aspects are acceptable demanded for a physically admissible star and satisfy all the required physical conditions. The stability of the model is also explored in the context of causality conditions, adiabatic index, generalized Tolman–Oppenheimer–Volkov (TOV) equation, Buchdahl Condition and Herrera Cracking Method. To show that the developed model is compatible with a wide range of recently observed pulsars, various relevant physical variables are also highlighted in tabular form. The data studied here are in agreement with the observation of gravitational waves from the first binary merger event. Assuming a particular surface density ( $$7.5 \times 10^{14}\text { gm cm}^{-3}$$ ), the mass-radius ( $$M - b$$ ) relationship and the radius-central density relationship ( $$b - \rho (0)$$ ) of the compact stellar object are analyzed for this model. Additionally, comparing the results with a slow rotating configuration, we have also discussed moment of inertia and the time period using Bejger-Haensel idea.