Narrow Results

In this study, we investigate the Bianchi type-I cosmologies with string cloud attached to perfect fluid in f(R) gravity. The field equations and their exact solutions for Bianchi type-I cosmologies with string cloud attached to a perfect fluid are found by using the conformal symmetry properties. The obtained solutions under the varied selection of arbitrary constants indicate three cosmological models. Isotropy conditions for obtained cosmological models are investigated for large value of time. Whether or not the string cloud in conformal symmetric Bianchi type-I universe supports the isotropy condition for the large value of time has been investigated. Also, we examine the contracting and decelerating features of the obtained solutions by using Raychaudhuri equation. Finally, geometrical and physical results of the solutions are discussed.

In this paper, we have examined charged strange quark matter attached to the string cloud in the spherical symmetric space–time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for spherical symmetric space–time with strange quark matter attached to the string cloud via conformal motions. Also, we have discussed the features of the obtained solutions.

We investigate spherically symmetric spacetime filled with global monopole and perfect fluid in $f(R)$-gravity. We consider field equations of $f(R)$-gravity in order to understand the global monopole and the perfect fluid curve to the spacetime. It has taken advantages of conformal symmetry properties of the spacetime to solve these equations. The obtained solutions are improved in case of phantom energy. It is shown that obtained $f(R)$ function is consistent with well-known models of the modified gravity. Also, it is examined whether the obtained solutions support a traversable wormhole geometry. Obtained results of the solutions have been concluded.

The current study examines the geometry of static wormholes with anisotropic matter distribution in the context of modified $f({𝒢})$ gravity. We consider the well-known Noether and conformal symmetries, which help in investigating wormholes in $f({𝒢})$ gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the $f({𝒢})$ gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified $f({𝒢})$ gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns.

The main emphasis of this paper is to find the viable solutions of Einstein Maxwell field equations of compact star in context of modified $f(R)$ theory of gravity. Two different models of modified $f(R)$ gravity are considered. In particular, we choose isotropic matter distribution and Bardeen’s model for compact star to find the boundary conditions as an exterior space-time geometry. We use the conformal Killing geometry to compute the metric potentials. We discuss the behavior of energy density and pressure distribution for both models. Moreover, we analyze different physical properties such as behavior of energy density and pressure, equilibrium conditions, equation of state parameters, causality conditions and adiabatic index. It is noticed that both $f(R)$ gravity models are suitable and provide viable results with Bardeen geometry.

The paper aims to investigate curvature inheritance (CI) symmetry in M-projectively flat spacetimes. It is shown that the CI symmetry in M-projectively flat spacetime is a conformal motion. We have proved that M-projective curvature tensor follows the symmetry inheritance property along a vector field $\xi$, when spacetime admits the conditions of both CI symmetry and conformal motion or motion along the vector field $\xi$. Also, we have derived some results for M-projectively flat spacetime with perfect fluid following the Einstein field equations (EFEs) with a cosmological term and admitting the CI symmetry along the vector field $\xi$. We have shown that an M-projectively flat perfect fluid spacetime obeying the EFEs with a cosmological term and admitting the CI symmetry along a vector field $\xi$ is either a vacuum or satisfies the vacuum-like equation of state. We have also shown that such spacetimes with the energy–momentum tensor of an electromagnetic field distribution do not admit any curvature symmetry of general relativity. Finally, an example of M-projectively flat spacetime has been exhibited.

The aim of this paper is to develop the isotropic and anisotropic quark stars configurations in the context of $f(T,{𝒯})$ gravity in the static spherically symmetric background. To explore the combined effects of torsion scalar $T$ and the trace of energy–momentum tensor (EMT) ${𝒯}$ on relativistic astrophysics, we use diagonal as well as non-diagonal tetrad fields. By considering the conformal Killing vectors along with the MIT bag model, the interior solutions of the field equations corresponding to the linear $f(T,{𝒯})=\alpha T(r)+\beta {𝒯}(r)+\varphi$ model (in which $\alpha ,\beta$ are the constants and $\varphi$ indicates the cosmological constant) are calculated. The feasibility of the obtained solutions is confirmed by implementing several physical tests. The model parameters are constrained subject to the existence and stability of the quark star models. We formulate the energy constraints, stability equations, mass function, compactness and redshift factor, and present the graphical analysis of all physical quantities. It is found that the derived solutions for both diagonal and non-diagonal tetrad exhibit well-behaved profiles in the framework of modified teleparallel gravity.