Accounting for exotic matter and the extreme radial tension in Morris–Thorne wormholes of embedding class one

The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein’s theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris–Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension at the throat.

Decoupled Embedding Class-One Strange Stars in Self-Interacting Brans–Dicke Gravity

This work aims to extend two isotropic solutions to the anisotropic domain by decoupling the field equations in self-interacting Brans–Dicke theory. The extended solutions are obtained by incorporating an additional source in the isotropic fluid distribution. We deform the radial metric potential to disintegrate the system of field equations into two sets such that each set corresponds to only one source (either isotropic or additional). The system related to the anisotropic source is solved by employing the MIT bag model as an equation of state. Further, we develop two isotropic solutions by plugging well-behaved radial metric potentials in Karmarkar’s embedding condition. The junction conditions at the surface of the star are imposed to specify the unknown constants appearing in the solution. We examine different physical characteristics of the constructed quark star models by using the mass and radius of PSR J1903+327. It is concluded that, in the presence of a massive scalar field, both stellar structures are well-behaved, viable and stable for smaller values of the decoupling parameter.

Possible Einstein’s cluster models in embedding class one spacetime

For the first time, we present Einstein’s cluster model in embedding class one spacetime. This paper shows that for any neutral configurations there is only one Einstein cluster solution in embedding class one. In fact, one can find two solutions where the first solution i.e. [Formula: see text] and [Formula: see text] is an unphysical one as it has zero density profile as well as violates the Pandey–Sharma condition (i.e. not a class one solution). However, the second solution can describe matter distribution representing Einstein’s cluster which is in static and equilibrium as it satisfies the static stability criterion and TOV-equation. The second solution not only satisfies the above conditions, but also satisfies the energy conditions. The equation of state parameter [Formula: see text] is less than unity signifying that it can represent physical matters. Further, we have also shown that the Einstein’s clusters may also exhibit the properties of compact stars.

Analysis of strange quark stars in massive Brans–Dicke gravity

In this paper, we explore the behavior and anisotropic structure of quark stellar models in the framework of massive Brans–Dicke gravity. The system of field equations, representing a static sphere, is formulated by incorporating the MIT bag model. We use the Karmarkar condition for embedding class-one to formulate a relativistic model corresponding to a well-behaved radial metric function. The values of unknown parameters are determined through the matching of internal and external space–times at the hypersurface. The observed masses and radii of the strange star candidates (RXJ 1856-37, Her X-1 and PSR J1614-2230) specify the solution. Further, we evaluate the impact of the massive scalar field on state parameters and investigate the viability as well as stability of the self-gravitating objects. It is found that the obtained values of the bag constant (corresponding to each star) lie within the accepted range. Moreover, the anisotropic structure meets the necessary viability and stability criteria.

Generating solutions for charged stellar models in general relativity

It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein–Maxwell equations may serve as generating functions for charged stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics, which do not depend on charge. In all these cases the equations are linear first order differential equations for one of the metric components and Riccati equations for the other. The latter may be always transformed into second order homogenous linear differential equations. These conclusions are illustrated by numerous particular examples from the study of charged stellar models.

Anisotropic compact stars via embedding approach in general relativity: new physical insights of stellar configurations

The main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential $$\lambda (r)$$ λ ( r ) , and we obtained the other metric potential $$\nu (r)$$ ν ( r ) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars.

Relativistic modeling of stellar objects using embedded class one spacetime continuum

In this paper, we explore a family of exact solutions to the Einstein field equations (EFEs) describing a spherically symmetric, static distribution of fluid spheres with pressure anisotropy in the setting of embedding class one spacetime continuum. A detailed theoretical analysis of this class of solutions for compact stars PSR J16142230, Her X-1, LMC X-4 and 4U 1538-52 is carried out. The solutions are verified by examining various physical aspects, viz., anisotropy, gravitational redshift, causality condition, equilibrium (TOV-equation), stable static criterion and energy conditions, in connection to their cogency. Due to the well-behaved nature of the solutions for a large range of positive real [Formula: see text] values, we develop models of above stellar objects and discuss their behavior with graphical representations of the class of solutions of the first two objects extensively. The solutions studied by Fuloria [Astrophys. Space Sci. 362, 217 (2017)] for [Formula: see text] and Tamta and Fuloria [Mod. Phys. Lett. A 34, 2050001 (2019), https://doi.org/10.1142/S0217732320500017 ] for [Formula: see text] are particular cases of our generalized solution.