Periodic Signature Change in Spacetimes of Embedding Class One

The idea of an oscillating Universe has remained a topic of interest even after the discovery of dark energy. This paper confirms this idea by means of another well-established theory in general relativity, the embedding of curved spacetimes in higher-dimensional flat spacetimes: an n-dimensional Riemannian space is said to be of embedding class m if m +n is the lowest dimension of the flat space in which the given space can be embedded;here . So a four-dimensional Riemannian space is of class two and can therefore be embedded in a six-dimensional flat space. A line element of class two can be reduced to a line element of class one by a suitable coordinate transformation. The extra dimension can be either spacelike or timelike, leading to accelerating and decelerating expansions, respectively. Accordingly, it is proposed in this paper that the free parameter occurring in the transformation be a periodic function of time. The result is a mathematical model that can be interpreted as a periodic change in the signature of the embedding space. This signature change may be the best model for an oscillating Universe and complements various models proposed in the literature.

A new class of viable and exact solutions of EFEs with Karmarkar conditions:an application to cold star modeling

In this work we present a theoretical framework within Einstein’s classical general relativity which models stellar compact objects such as PSR J1614-2230 and SAX J1808.4-3658.The Einstein field equations are solved by assuming that the interior of the compact object is described by a class I spacetime.The so-called Karmarkar condition arising from this requirement is integrated to reduce the gravitational behaviour to a single generating function.By appealing to physics we adopt a form for the gravitational potential which is sufficiently robust to accurately describe compact objects.Our model satisfies all the requirements for physically realistic stellar structures.

On the Spectrum of a Class of Differential Operators and Embedding Theorems

The author considers the embedding problem of weighted Sobolev spaces Hnp in weighted Ls spaces Ls,r,and some sufficient conditions and necessary conditions are given, when weight functions satisfy certain conditions.The author uses the results obtained to the qualitative analysis of the spectrum of 2n-order weighted differential operator,and gives some sufficient conditions and necessary conditions to ensure that the spectrum is discrete.

Relativistic models of anisotropic superdense star in the regime of Karmarkar's condition

We obtained a new class of solutions for a relativistic anisotropic compact star by utilizing the Karmarkar embedding condition.To obtain the closed-form solution a suitable form of one of the gravitational potentials has been chosen to determine the other by analyzing the Karmarkar condition.The resulting solutions are found to be well-behaved and regular and could describe a compact stellar object.Considering the current estimated values of the mass and radius of the pulsar 4U1820-30 as input parameters,all the physically relevant parameters are shown to be well-behaved to a very good degree of accuracy.

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.

Anisotropic stars in modified gravity:An extended gravitational decoupling approach

In this study,we conduct an investigation on decoupling gravitational sources under the framework of f(R,T)gravity.Basically,the complete geometric deformation technique is employed,which facilitates finding the exact solutions to the anisotropic astrophysical system smoothly without imposing any particular ansatz for the deformation function.In addition,we used 5-dimensional Euclidean spacetime in order to describe the embedding Class Ⅰ spacetime in order to obtain a solvable spherical physical system.The resulting solutions are both physically interesting and viable with new possibilities for investigation.Notably,the present investigation demonstrates that the mixture of f(R,T)+CGD translates to a scenario beyond the pure GR realm and helps to enhance the features of the interior astrophysical aspects of compact stellar objects.To determine the physical acceptability and stability of the stellar system based on the obtained solutions,we conducted a series of physical tests that satisfied all stability criteria,including the nonsingular nature of density and pressure.