[en] We propose a new model of dark energy star consisting of five zones, namely, the solid core of constant energy density, the thin shell between core and interior, an inhomogeneous interior region with anisotropic pressures, a thin shell, and the exterior vacuum region. We discuss various physical properties. The model satisfies all the physical requirements. The stability condition under a small linear perturbation is also discussed. (orig.)

[en] In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)

[en] We construct a cylindrical symmetry vacuum solution of the Einstein field equations, regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The geodesics motion of free test particles near the singularity, geodesic expansion to understand the nature of singularity, and the C-energy of the vacuum metric, will be discussed. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented. (orig.)

[en] We present Tolman IV spacetime representing compact fluid sphere in bigravity. Here, we have explored the effect of scale parameter k in the local matter distribution of compact stars. We have modelled for three well-known compact stars, and it shows that lower values of k lead to stiffer EoS. This claim is also supported by the graphical analysis. It can be observed that the sound speed and the adiabatic index are more for lower values of k. It is also seen that all the solutions of Einstein’s field equations are still satisfying the field equations in the presence of a background metric ${\mathrm{\gamma <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}\mathrm{\nu <!--\; ??\; -->}}$. However, the density and pressure are modified by extra term from the constant curvature background, thus affecting the EoS. One can also think that the parameter $\mathrm{\alpha <!--\; ??\; -->}\equiv <!--\; ???\; -->1/k^2$ as coupling constant between the $g_{\mathrm{\mu <!--\; ??\; -->}\mathrm{\nu <!--\; ??\; -->}}$ and ${\mathrm{\gamma <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}\mathrm{\nu <!--\; ??\; -->}}$ and consequently more the coupling stiffer is the EoS. As $k\to <!--\; ???\; -->\mathrm{\infty <!--\; ???\; -->}$, the background de Sitter spacetime reduces to Minkowski’s spacetime and the coupling vanishes. The solution satisfies the causality condition, all the energy conditions and equilibrium under gravity and hydrostatic forces. The stability of the local stellar structure is enhanced by reducing the scalar curvature of the background spacetime.

[en] In this article, we discuss four dimensional non-static space-times in the background of de-Sitter and anti-de Sitter spaces with the matter-energy sources as a stiff fluid, anisotropic fluid, and an electromagnetic field. Under various parameter conditions the solutions may represent models of naked singularity and/or black holes. Finally, the energy-momentum distributions using the complexes of Landau-Lifshitz, Einstein, Papapetrou, and Moeller prescriptions, were evaluated. (orig.)

[en] Bianchi type VI₀ cosmological model in the presence of the electromagnetic field in the theory of relativity is studied. For the current flow along z-axis, 𝐹₁₂ is the only nonvanishing component of 𝐹_𝑖𝑗 (the magnetic field). An exact solution of the field equations is given by considering the deceleration parameter as a linear function of t in the form 𝑞=−1+𝑚−𝑘𝑡 where m and k are constants. The entropy 𝐒 and the thermodynamic functions (enthalpy, Gibbs energy and Helmholtz energy) of the universe are calculated and studied. Also, physical and geometrical properties of our models are studied. (author)

[en] We here investigate a cosmological model in which three fluids interact with each other, involving certain coupling parameters and energy exchange rates. The motivation of the problem stems from the puzzling 'triple coincidence problem' which naively asks why the cosmic energy densities of matter, radiation and dark energy are almost of the same order of magnitude at the present time. In our model, we determine the conditions under which triple interacting fluids will cross the phantom divide. (orig.)

[en] In this paper, we show that no solutions exist for Bianchi type ${\text{VI}}_0$ cosmological model in the modified gravity theories, namely in self-creation theory and in gravity theory based on Lyra geometry under the two physical conditions: The pressure p and the density $\mathrm{\rho <!--\; ??\; -->}$ of the fluid are related by the equation of state $p=\mathrm{\lambda <!--\; ??\; -->}\mathrm{\rho <!--\; ??\; -->},0\le <!--\; ???\; -->\mathrm{\lambda <!--\; ??\; -->}\le <!--\; ???\; -->1,$ and the scalar expansion $\mathrm{\Theta <!--\; ??\; -->}$ of the cosmological model is proportional to the eigenvalue ${\mathrm{\sigma <!--\; ??\; -->}}_3^3$ of the shear tensor. In self-creation theory, only the possible solutions are found for dust and radiation cases. Physical and geometrical properties of the obtained models are discussed for different cases of matter distribution. Also, we study the effect of the scalar field $\mathrm{\varphi <!--\; ??\; -->}$ on the entropy $\mathbf{S}$ of our universe with an expression for the entropy for all different cases of matter distribution. Also we have proved that the Lyra term has no effect on the entropy of the universe.

[en] In the present work, we have searched for the existence of anisotropic and non-singular compact star in the f(R,T) gravity by taking into account the non-exotic equation of state (EoS). In order to obtain the solutions of the matter content of the compact object, we assume the well-known barotropic form of EoS that yields the linear relation between pressures and energy density. We propose the existence of non-exotic compact star which shows the validation of energy conditions and stability within the perspective of f(R,T) extended theory of gravity. The linear material correction in the extended theory and matter content of compact star can remarkably satisfy energy condition. We discuss various physical features of the compact star and show that the proposed model of the stellar object satisfies all regularity conditions and is stable as well as singularity-free. (author)

[en] In this paper, we propose the braneworld gravastar configuration which is an alternative to the braneworld black hole. We study the Mazur and Mottola gravastar model within the context of the Randall-Sundrum type II braneworld scenario, based on the fact that our four dimensional spacetime is a three-brane, embedded in a five dimensional bulk. We present exact solutions of the modified field equations in each of the three regions making up the gravastar, namely, (I) the core, (II) the shell, and (III) the vacuum exterior. The junction conditions at each interface are fulfilled and we further explore interesting physical properties such as length, energy and entropy of the spherical distribution. (orig.)