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We study spherically symmetric timelike thin-shells in $3+1$-dimensional bulk spacetime with a variable equation-of-state for the fluid presented on the shell. In such a fluid, the angular pressure $p$ is a function of both surface energy density $\sigma$ and the radius $R$ of the thin-shell. Explicit cases of the thin shells connecting two nonidentical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.

A Finsler metric F is said to be spherically symmetric if the orthogonal group O(n) acts as isometries of F. In this paper, we show that every spherically symmetric Finsler metric of isotropic Berwald curvature is a Randers metric. We also construct explicitly a lot of new isotropic Berwald spherically symmetric Finsler metrics.

We consider the distribution of spherically symmetric self-gravitating non-dissipative (but anisotropic) fluids under the expansion-free condition which requires the existence of vacuum cavity within the fluid distribution. The Darmois junction condition is investigated for matching the spherically symmetric metric to an internal vacuum cavity (Minkowski space-time). We have studied some analytical models, total of three family of solutions out of which two satisfy the junction conditions over both the hypersurfaces. The models are investigated under some known dynamical assumptions which further provide analytical solution in each family.

This study deals with the spherically symmetric radiating star (with dissipative perfect fluids) with a central vacuum cavity, evolving under the assumption of expansion-free motion. The analytical model of the such dynamics star is discussed in three regimes — diffusion approximation, geodesic motion and self-similarity — and the solutions of dynamical equations are obtained in its complete generality. The structure scalars, which are related to the fundamental properties of fluid distribution, are also discussed which played a very important role in the dynamics of cavity models. It has been shown that energy density is homogeneous but violates the energy condition under quasi-static diffusion approximation.

With due consideration of reasonable cosmological assumptions within the limit of the present cosmological scenario, we have analyzed a spherically symmetric metric in 5D setting within the framework of Lyra manifold. The model universe is predicted to be a DE model, dominated by vacuum energy. The model represents an oscillating model, each cycle evolving with a big bang and ending at a big crunch, undergoing a series of bounces. The universe is isotropic and undergoes super-exponential expansion. The value of Hubble’s parameter is measured to be $H=67.0691$ which is very close to $H_0=67.36\pm 0.54\mathrm{\text{km}}{\mathrm{\text{s}}}^{-1}{\mathrm{\text{Mpc}}}^{-1}$, the value estimated by the latest Planck 2018 result. A detailed discussion on the cosmological parameters obtained is also presented with graphs.

In astrophysics studies, the stellar system (e.g. stars, etc.) is generally considered a spherically symmetric object, and its evolutions (e.g. collapse) depends on the nature of fluid distribution and kinematical properties that are not precisely known. One generally makes additional restrictions allowing the integration of the field equations for the studies of dynamical models. This work deals with the spherically symmetric stellar system with uniform expansion scalar ($\mathrm{\Theta }$) describing the uniform collapse of stars. The uniform expansion scalar describes an important physical scenario (a generalization of the OSD model) that will exhibit a new class of collapsing stars. Here, we have parameterized the expansion scalar as exponential, power law and their combination form as a function of time $t$ so that it describes the collapsing configuration $(\mathrm{\Theta }<0)$. The formation of black-hole, the horizon surface, and the thermal behavior of black-hole has also been discussed. Further, we have discussed the dynamics of uniformly collapsing system for conformally flatness. The uniform motion (collapse) of any stellar system is a fascinating phenomenon therefore the present works will produce new aspects for the studies of collapsing stellar systems and may generate broad interest among astrophysicists.

We consider it worthy if we could construct a realistic model universe that would enable us to identify a clue about the source of dark energy. So, we develop a Scale Covariant Theory model universe considering a 5D spherically symmetric space-time. It is predicted that the constructed model itself behaves as a phantom energy model/ source that tends to a de Sitter phase avoiding the finite-time future singularity (big rip). The model universe is isotropic and is free from an initial singularity. The gravitational constant $G$ decreases with a variation of $-7.2\times 10^{-11}$${\mathrm{\text{yr}}}^{-1}$ and the Hubble parameter is estimated to be $H=68$. We also provide a thorough analysis of the cosmological findings with graphical representations.