Anisotropic compact stars in Karmarkar spacetime

We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of Class One reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the grr metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We use this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348＋0432, PSR B0943＋10and XTE J1739-285.

Exploring physical properties of compact stars in f(R,T)-gravity:An embedding approach

Solving field equations exactly in f(R,T)−gravity is a challenging task.To do so,many authors have adopted different methods such as assuming both the metric functions and an equation of state(EoS)and a metric function.However,such methods may not always lead to well-behaved solutions,and the solutions may even be rejected after complete calculations.Nevertheless,very recent studies on embedding class-one methods suggest that the chances of arriving at a well-behaved solution are very high,which is inspiring.In the class-one approach,one of the metric potentials is estimated and the other can be obtained using the Karmarkar condition.In this study,a new class-one solution is proposed that is well-behaved from all physical points of view.The nature of the solution is analyzed by tuning the f(R,T)−coupling parameterχ,and it is found that the solution leads to a stiffer EoS forχ=−1 than that forχ=1.This is because for small values ofχ,the velocity of sound is higher,leading to higher values of Mmax in the M−R curve and the EoS parameterω.The solution satisfies the causality condition and energy conditions and remains stable and static under radial perturbations(static stability criterion)and in equilibrium(modified TOV equation).The resulting M−R diagram is well-fitted with observed values from a few compact stars such as PSR J1614-2230,Vela X-1,Cen X-3,and SAX J1808.4-3658.Therefore,for different values ofχ,the corresponding radii and their respective moments of inertia have been predicted from the M−I curve.

Static fluid spheres admitting Karmarkar condition

We explore a new relativistic anisotropic solution of the Einstein field equations for compact stars based on embedding class one condition.For this purpose,we use the embedding class one methodology by employing the Karmarkar condition.Employing this methodology,we obtain a particular differential equation that connects both the gravitational potentials e^λ and e^ν.We solve this particular differential equation choosing a simple form of generalized gravitational potential grr to describe a complete structure of the space-time within the stellar configuration.After determining this space-time geometry for the stellar models,we discuss thermodynamical observables including radial and tangential pressures,matter density,red-shift,velocity of sound,etc.,in the stellar models.We also perform a complete graphical analysis,which shows that our models satisfy all the physical and mathematical requirements of ultra-high dense collapsed structures.Further,we discuss the moment of inertia and M-R curve for rotating and non-rotating stars.