In the present article, we have constructed static anisotropic compact star models of Einstein field equations for the spherical symmetric metric of embedding class one. By assuming the particular form of metric function ν, We have solved the Einstein field equations for anisotropic matter distribution. The anisotropic models are representing the realistic compact objects such as SAX J 1808.4-3658 (SS1), Her X -1, Vela X-12, PSR J1614-2230 and Cen X -3. We have reported our results in details for compact star Her X-1 on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, TOV equation and red-shift etc. Along with these, we have also discussed about stability of the compact star models. Finally we made the comparison between our anisotropic stars with the realistic objects on the key aspects as central density, central pressure, compactness and surface red-shift.

In the present paper we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function e λ and solved the Einstein's relativistic field equations with the help of Karmarkar condition for an anisotropic matter distribution. The physical properties of our model such as pressure, density, mass function, surface red-shift, gravitational red-shift are investigated and the stability of the stellar configuration is discussed in details. Our model is free from central singularities and satisfies all energy conditions. The model we present here satisfy the static stability criterion i.e. dM/dρc > 0 for 0 ≤ ρc ≤ 4.04 × 10 17 g/cm 3 (stable region) and for ρc ≥ 4.04 × 10 17 g/cm 3 , the region is unstable i.e., dM/dρc ≤ 0.

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In this article, we study the possibility of sustaining static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of the detection of wormholes in the outer regions of galactic halos by means of gravitational lensing. Studies of the total gravitational energy for the exotic matter inside a static wormhole configuration are also performed.

In present paper a spherically symmetric stellar configuration has been analyzed by assuming the matter distribution of the stellar configuration is anisotropic in nature and compared with the realistic objects, namely, the low mass X-ray binaries (LMXBs) and X-ray pulsars. The analytic solution has been obtained by utilizing the dark energy equation of state for the interior solution corresponding to the Schwarzschild exterior vacuum solution at the junction interface. Several physical properties like energy conditions, stability, mass-radius ratio, and surface redshift are described through mathematical calculations as well as graphical plots. It is found that obtained mass-radius ration of the compact stars candidates like 4U 1820-30, PSR J 1614-2230, Vela X-1 and Cen X3are very much consistent with the observed data by Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431, 3216 (2013)). So our proposed model would be useful in the investigation of the possible clustering of dark energy.

The prospect of identifying wormholes by investigating the shadows of wormholes constitute a foremost source of insight into the evolution of compact objects and it is one of the essential problems in contemporary astrophysics. The nature of the compact objects (wormholes) plays a crucial role on shadow effect, which actually arises during the strong gravitational lensing. Current Event Horizon Telescope observations have inspired scientists to study and to construct the shadow images of the wormholes. In this work, we explore the shadow cast by a certain class of rotating wormhole. To search this, we first compose the null geodesics and study the effects of the parameters on the photon orbit. We have exposed the form and size of the wormhole shadow and have found that it is slanted as well as can be altered depending on the different parameters present in the wormhole spacetime. We also constrain the size and the spin of the wormhole using the results from M87* observation, by investigating the average diameter of the wormhole shadow as well as its deviation from circularity with respect to the wormhole throat size. In a future observation, this type of study may help to indicate the presence of a wormhole in a galactic region.

In this paper, we have investigated the classical tests of General Relativity like precession of perihelion, deflection of light and time delay by considering a phenomenological astrophysical object like Sun, as a neutral regular Hayward black hole in Rastall gravity. We have tabulated all our results for some appropriate values of the parameter [Formula: see text]. We have compared our values with [Formula: see text], which corresponds to the Schwarzschild case. Also the value of [Formula: see text] is of particular interest as it gives some promising results.