The superdense stars with mass-to-size ratio exceeding 0.3 are expected to be made of strange matter. Assuming that the 3-space of the interior space-time of a strange star is that of a three-paraboloid immersed in a four-dimensional Euclidean space, we obtain a two-parameter family of their physically viable relativistic models. This ansatz determines density distribution of the interior self-gravitating matter up to one unknown parameter. The Einstein's field equations determine the fluid pressure and the remaining geometrical variables. The information about mass-to-size ratio together with the conventional boundary conditions lead to the determination of total mass, radius and other parameters of the stellar configuration.

The physically viable models of compact stars like SAX (J1808.4-3658) can be obtained using Vaidya–Tikekar ansatz prescribing spheroidal geometry for their interior space–time. We discuss here the suitability of an alternative ansatz in this context. The models of superdense star are proposed using a general three parameter family of solutions of relativistic field equations obtained adopting the alternative ansatz. The setup is shown to admit physically viable models of superdense stars and strange matter stars such as Her. X-1.

The objective of this paper is to find out the suitability of an ansatz similar to that suggested by Vaidya–Tikekar, but prescribing paraboloidal geometry for the 3-space of the interior space–time of a relativistic spherical star in describing a family of physically viable models of superdense stars like Her X-1, SAX, and X-ray brust.

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Cylindrically symmetric inhomogeneous magnetized string cosmological model is investigated with cosmological term Λ varying with time. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ 1 1 of the shear tensor σ i j . The value of cosmological constant for the model is found to be small and positive which is supported by the results from recent supernovae Ia observations. The physical and geometric properties of the model are also discussed in presence and absence of magnetic field.

We present two dark energy (DE) models with an anisotropic fluid in Bianchi type-V I 0 space-time by considering time dependent deceleration parameter (DP). The equation of state (EoS) for dark energy ω is found to be time dependent and its existing range for derived models is in good agreement with the recent observations. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the EoS parameter for DE changes from ω > −1 to ω = −1 in first model whereas from ω > −1 to ω < −1 in second model which is consistent with recent observations. The cosmological constant is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent type Ia supernovae observations. The cosmic jerk parameter in our derived models is also found to be in good agreement with the recent data of astrophysical observations. The physical and geometric aspects of both the models are also discussed in detail.

The Bañados, Teitelboim and Zanelli[1] solution corresponding to the exterior space-time of a black hole in (2 + 1) dimensions has been found to be very useful to understand various aspects relating to the gravitational field of a black hole. We present here a class of interior solutions corresponding to the BTZ exterior by making use of a model presented by Finch and Skea[2] which was earlier found to be relevant for the description realistic stars in (3 + 1) dimensions. We show physical viability of the model in lower dimensions as well.

In this paper we have obtained some new exact solutions of Einstein's field equations in a spatially homogeneous and anisotropic Bianchi type-V space-time with perfect fluid distribution along with heat-conduction and decaying vacuum energy density by applying the variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter. We find that the constant value of deceleration parameter is reasonable for the present day universe. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein's field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The cosmological constant is found to be a decreasing function of time and positive which is corroborated by results from recent supernovae Ia observations. Expressions for lookback time-redshift, neoclassical tests (proper distance d(z)), luminosity distance red-shift and event horizon are derived and their significance are described in detail. The physical and geometric properties of spatially homogeneous and anisotropic cosmological models are discussed.