Gravastars have been considered as a feasible alternative to black holes in the past couple of decades. Stable models of gravastar have been studied in many of the alternative gravity theories besides standard General Relativity (GR). The Rastall theory of gravity is a popular alternative to GR, specially in the cosmological and astrophysical context. Here, we propose a stellar model under the Rastall gravity following Mazur-Mottola's \cite{Mazur2001,Mazur2004} conjecture. The gravastar consists of three regions, viz., ($I$) Interior region, ($II$) Intermediate shell region, and ($III$) Exterior region. The pressure within the interior core region is assumed with a constant negative matter-energy density which provides a repulsive force over the entire thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma which follows the Zel'dovich's conjecture of stiff fluid \cite{Zeldo1962,Zel'dovich1972}. It is also assumed that the pressure is proportional to the matter-energy density according to Zel'dovich's conjecture, which cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum which is described by the Schwarzschild-de Sitter solution. Under all these specifications we obtain a set of exact and singularity-free solutions of the gravastar model presenting several physically valid features within the framework of Rastall gravity. The physical properties of the shell region namely, the energy density, proper length, total energy and entropy are explored. The stability of the gravastar model is investigated using the surface redshift against the shell thickness and maximizing the entropy of the shell within the framework of Rastall gravity.

Study of gravastars in Rastall gravity

This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the $f(\tau, T)$ gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within $f(\tau,T)$ gravity to investigate traversable wormholes. In particular, we discuss the possible cases for the wormhole geometries using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, we discuss different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, we provide the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions.

Traversable Wormholes in the Extended Teleparallel Theory of Gravity with Matter Coupling

We review recent works on the possibility for eternal existence of thin-shell wormholes on Einstein and Einstein–Gauss–Bonnet gravity. We introduce thin-shell wormholes that are categorized into a class of traversable wormhole solutions. After that, we discuss stable thin-shell wormholes with negative-tension branes in Reissner–Nordstrom–(anti) de Sitter spacetimes in d-dimensional Einstein gravity. Imposing Z2 symmetry, we construct and classify traversable static thin-shell wormholes in spherical, planar and hyperbolic symmetries. It is found that the spherical wormholes are stable against spherically symmetric perturbations. It is also found that some classes of wormholes in planar and hyperbolic symmetries with a negative cosmological constant are stable against perturbations preserving symmetries. In most cases, stable wormholes are found with the appropriate combination of an electric charge and a negative cosmological constant. However, as special cases, there are stable wormholes even with a vanishing cosmological constant in spherical symmetry and with a vanishing electric charge in hyperbolic symmetry. Subsequently, the existence and dynamical stability of traversable thin-shell wormholes with electrically neutral negative-tension branes is discussed in Einstein–Gauss–Bonnet theory of gravitation. We consider radial perturbations against the shell for the solutions, which have the Z2 symmetry. The effect of the Gauss–Bonnet term on the stability depends on the spacetime symmetry.

https://www.mdpi.com/2218-1997/6/11/197/pdf

Thin-Shell Wormholes in Einstein and Einstein–Gauss–Bonnet Theories of Gravity

Charged strange stars with dust and phantom regimes in Rastall gravity

Study of Gravastars in Rastall Gravity

Non-commutative wormholes exhibiting conformal motion in Rastall gravity

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Non-commutative wormholes exhibiting conformal motion in Rastall gravity