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The Vaidya and Tikekar (1982) ansatz has so far provided numerous stellar solutions which are useful for the description of compact stars like neutron stars and quark stars. We re-examine the impacts of the spacetime curvature parameter of the Vaidya–Tikekar ansatz on the physical properties of the relativistic anisotropic star. For a spherically symmetric, static and anisotropic stellar configuration, in the Vaidya–Tikekar background spacetime, we develop new exact solutions by assuming a polytropic type equation of state p r = k ρ 1 + 1 n − β. Recent data from observed pulsars are taken as input parameters to validate the developed model. We examine the impact of the spheroidal curvature parameter of the VT spacetime on the stellar behaviour and mass–radius (M–R) relationship. It is observed that with the increase in the departure from spherical geometry, values of physical quantities, such as density and pressure, increase. • We have found a stable model of compact stars and fulfils all the regularity conditions and physical requirements. • An interesting feature of the model is that it provides a free parameter K, which makes it suitable for the description of a wide range of compact stars. [ABSTRACT FROM AUTHOR]

• Oscillations can be generated in neutron stars through tidal interactions. • These stellar oscillations can be detected through gravitational waves. • These oscillations can be studied using simulations of evolution of perturbed stars. • The fundamental mode varies for different equations of state of the stellar matter. In this study, we perform full three dimensional numerical relativity simulations of non-rotating general relativistic stars. Extending the studies for polytropic equation of state, we investigate the accuracy and robustness of numerical scheme on measuring fundamental (f)-mode frequency for realistic equations of state (EoS). We use various EoS with varying range of stiffness and numerically evolve perturbed stellar models for several mass configurations (in the range of 1.2 − 2.0 M ⊙) for each of these EoS. Using the gravitational waveform obtained from the simulations we extract the f -modes of the stars. The obtained results are tested against the pre-existing perturbation methods and find good agreement. Validity and deviation of universal relations have been carried out and are compared with earlier results under Cowling approximation as well as perturbative approaches. We also show that even using perturbed single star simulations can provide good agreement with f -modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive. [ABSTRACT FROM AUTHOR]

• We have formulated the new physical generalized polytropic models. • We have assumed the Finch-Skea spacetime to develop the compact star models. • The proposed models fulfills all criteria for physical adequacy. • Distinct physical features of the obtained models have been examined and evaluated. • We have used the linear, quadratic and polytropic equation of state. In present article, we have formulated the new physical generalized polytropic models with anisotropic matter distribution in the absence of electromagnetic field. We have assumed the Finch-Skea spacetime to develop the models, which fulfill all the criteria for the physical adequacy. Distinct physical features of the obtained models have been examined and evaluated. Furthermore, the physical quantities are presented graphically to meet the physical conditions of viable astronomical models. These results can be reduced to the different cases of uncharged anisotropic fluid such as linear, quadratic and polytropic equations of state. [ABSTRACT FROM AUTHOR]

• Two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry are studied. • The validity of the solutions is verified by performing several physical tests. • The solutions satisfy all the physical requirements necessary for well-behaved models. • The models represent neutron star in Vela X-1. In this paper, we present two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry. The solutions are composed of two parts: The inner region of the star is described by class I Karmarkar space-time, while exterior of the star is characterized by both the Bardeen and the Reissner–Nordstrom space-times. Physical analysis of the matter and thermodynamical variables show that the models are well-behaved. For our parametric set of values, we conclude that the Bardeen black hole metric can be used as an alternate to the exterior Reissner–Nordstrom metric. [ABSTRACT FROM AUTHOR]

• The compact stars Construction with Tolman-Kuchowicz Spacetime in f (R , G) Gravity is discussed. • The anisotropic source of matter has considered for this study. • By making use of field equations, many physical aspects have been discussed. • Some physical aspects are explored under the particular parametric values. In this paper, we review some anisotropic stellar spheres in the framework of modified f (R , G) gravity. For this purpose, we have capitalized the Tolman-Kuchowicz spacetime Tolman (1939) ; Kuchowicz (1968). The equations of motion have been formulated by considering anisotropic matter distribution along with metric potentials, a = B r 2 + 2 l n C and b = l n (1 + α r 2 + β r 4). To determine the new constraints, observational data of 4 U 1538 − 52 , H e r X − 1 and S A X J 1808.4 − 3658 have been pre-owned. Dynamical equations have been evaluated by making use of Starobinsky model f (R , G) = R + λ R 2 + G 2. Many physical aspects have been enlightened, such as energy density, pressure evolutions, adiabatic index, TOV equations and surface redshift. The credibility of our presented model has been confirmed by observing the evolution of some physical aspects and it is concluded that our system is free from all singularities and is physically stable. [ABSTRACT FROM AUTHOR]

• We have obtained a new parametric class of well-behaved solutions in embedding class I. • We use pressure anisotropy and Karmarkar condition for developing viable models of compact stars PSR J1614-2230 and SAX J1808.4-3658. • Our solutions satisfy the following stability conditions i.e., Herrera cracking condition, causality condition, Bondi condition, Zeldovich condition and stable static criteria (Harrison-Zeldovich-Novikov criterion) for both the stars in their respective ranges of parametric class. • Our solutions satisfy all energy conditions and equilibrium condition (TOV equation) which are essential for a physically viable stellar models. The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency. [ABSTRACT FROM AUTHOR]