We propose a unique stellar model under the f (R, T ) gravity by using the conjecture of MazurMottola [P. Mazur and E. Mottola, Report number: LA-UR-01-5067., P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545 (2004).] which is known as gravastar and a viable alternative to the black hole as available in literature. This gravastar is described by the three different regions, viz., (I) Interior core region, (II) Intermediate thin shell, and (III) Exterior spherical region. The pressure within the interior region is equal to the constant negative matter density which provides a repulsive force over the thin spherical shell. This thin shell is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel'dovich's conjecture of stiff fluid [Y.B. Zel'dovich, Mon. Not. R. Astron. Soc. 160, 1 (1972).], does counterbalance the repulsive force exerted by the interior core region. The exterior spherical region is completely vacuum and assumed to be de Sitter spacetime which can be described by the Schwarzschild solution. Under this specification we find out a set of exact and singularity-free solution of the gravastar which presents several other physically valid features within the framework of alternative gravity.

In the present paper we generate a set of solutions describing the interior of a compact star under f (R, T ) theory of gravity which admits conformal motion. An extension of general relativity, the f (R, T ) gravity is associated to Ricci scalar R and the trace of the energy-momentum tensor T . To handle the Einstein field equations in the form of differential equations of second order, first of all we adopt the Lie algebra with conformal Killing vectors (CKV) which enable one to get a solvable form of such equations and second we consider the equation of state (EOS) p = ωρ with 0 < ω < 1 for the fluid distribution consisting of normal matter, ω being the EOS parameter. We therefore analytically explore several physical aspects of the model to represent behavior of the compact stars such as-energy conditions, TOV equation, stability of the system, Buchdahl condition, compactness and redshift. It is checked that the physical validity and the acceptability of the present model within the specified observational constraint in connection to a dozen of the compact star candidates are quite satisfactory.

We have proposed a model for relativistic compact star with anisotropy and analytically obtained exact spherically symmetric solutions describing the interior of the dense star admitting non-static conformal symmetry. Several features of the solutions including drawbacks of the model have been explored and discussed. For this purpose we have provided the energy conditions, TOV-equations and other physical requirements and thus thoroughly investigated stability, mass-radius relation and surface redshift of the model. It is observed that most of the features are well matched with the compact stars, like quark/strange stars.

Following the recent theory of f(Q) gravity, we continue to investigate the possible existence of wormhole geometries, where Q is the non-metricity scalar. Recently, the non-metricity scalar and the corresponding field equations have been studied for some spherically symmetric configurations in Mustafa (Phys Lett B 821:136612, 2021) and Lin and Zhai (Phys Rev D 103:124001, 2021). One can note that field equations are different in these two studies. Following Lin and Zhai (2021), we systematically study the field equations for wormhole solutions and found the violation of null energy conditions in the throat neighborhood. More specifically, considering specific choices for the f(Q) form and for constant redshift with different shape functions, we present a class of solutions for static and spherically symmetric wormholes. Our survey indicates that wormhole solutions could not exist for specific form function $$f(Q)= Q+ \alpha Q^2$$ f ( Q ) = Q + α Q 2 . To summarize, exact wormhole models can be constructed with violation of the null energy condition throughout the spacetime while being $$\rho \ge 0$$ ρ ≥ 0 and vice versa.

In this paper a Banados, Teitelboim and Zanelli (BTZ) black hole is constructed from an exact solution of the Einstein field equations in a (2+1)-dimensional anti-de Sitter spacetime in the context of noncommutative geometry. The BTZ black hole turns out to have two horizons, no horizon or a single horizon corresponding to a minimal mass. Certain thermodynamical properties are investigated, including Hawking temperature, entropy and heat capacity. Also discussed is the geodesic structure of BTZ black holes for both massless and massive particles. In particular, it is shown that bound orbits for test particles are possible.Comment: 8 pages, 10 figures, Minor changes in the text, Accepted in Physical Review

In this work, a physically reasonable metric potential g rr and a specific choice of the anisotropy has been utilized to obtain closed-form solutions of the Einstein field equation for a spherically symmetric anisotropic matter distribution. This class of solution has been used to develop viable models for observed pulsars. Smooth matching of interior spacetime metric with the exterior Schwarzschild metric and utilizing the condition that radial pressure is zero across the boundary leads us to determine the model parameters. A particular pulsar 4U 1820 − 30 having current estimated mass and radius (mass = 1.58M and radius = 9.1 km) has been allowed for testing the physical acceptability of the developed model. The gross physical nature of the observed pulsar has been analyzed graphically. The stability of the model is also discussed given causality conditions, adiabatic index and generalized Tolman-Oppenheimer-Volkov (TOV) equation under the forces acting on the system. To show that this model is compatible with observational data, few more pulsars have been considered, and all the requirements of a realistic star are highlighted. Additionally, the mass-radius (M-R) relationship of compact stellar objects analyzed for this model. The maximum mass for the presented model is ≈ 4M which is compared with the realization of Rhoades and Ruffini (Phys Rev Lett 32:324, 1974).

We present here a detailed analysis on the effects of charge on the anisotropic strange star candidates by considering a spherically symmetric interior spacetime metric. To obtain exact solution of the Einstein-Maxwell field equations we have considered the anisotropic strange quark matter (SQM) distribution governed by the simplified MIT bag equation of state (EOS), p = 1 3 (ρ − 4 B), where B is the bag constant and the distribution of the electrical charge is given as q(r) = Q (r/R) 3 = αr 3 , where α is a cona

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