This work mainly focuses on unveiling the particle dynamics features of black holes. For this objective, we utilize the charged black hole geometry consisting of the cloud strings and quintessence under the ansatz of Rastall gravity. We have calculated and analyzed the effective potential, angular momentum, particle energy, horizon radius, inner stable circular orbit, photon sphere radius, quasi-periodic oscillations, and effective force to reveal the dynamical features. We in detail discussed the effects of charge in black hole, Rastall parameter, strings of cloud parameter, and quintessential parameter on the calculated results. To ensure the scenario of accelerated expansion, ω _q lies in the range −1 < ω _q < −1/3. From this specific range, we choose ω _q = −2/3.

The present study is devoted to explore the existence of a new family of compact star solutions by adopting the Karmarkar as well as Pandey–Sharma condition in the background of $f(\mathcal{R},\mathcal{T})$ modified gravitational framework. For this purpose, we consider static spherically symmetric spacetime with anisotropic fluid distribution in absence of electric charge. In respect of Karmarkar condition, we assume a specific model of $g_{rr}$ metric potential representing a new family of solutions which is also compatible with the Pandey–Sharma condition. This assumed model permits us to calculate the $g_{tt}$ component of metric tensor by making the use of Karmarkar condition. Further, we investigate the interior solutions for $VelaX-1$ model of compact star by utilizing this new family of solutions for different values of parameter $\lambda$ . We have tuned the solution for $VelaX-1$ so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. It is found that these solutions fulfill all the necessary conditions under the observational radii and mass attribute data for small values of parameter $\lambda$ and hence physically well-behaved and promising. Through graphical analysis, it is observed that our obtained analytical solutions are physically acceptable with a best degree of accuracy for $n\in [1.8,7)-\{2,4,6\}$ , where parameter n is involved in the discussed model. It is also noticed the causality condition is violated for all $n\ge 7$ and the tangential sound velocity $v_t$ is observed as complex valued for all $0<n<1.8$ . Likewise, we explore these properties by considering large parameter $\lambda$ values. It is seen that the presented model violates all the physical conditions for $n\in \{2,4,6\}$ , while some of these for large values of $\lambda$ . Consequently, it can be concluded that the parameters n and $\lambda$ have a strong impact on the obtained solutions.

In this paper, black hole solutions are developed within the framework of f(R, T) gravity through the minimal gravitational decoupling approach. By introducing a new source in the original isotropic matter distribution, the corresponding field equations acquire additional degrees of freedom. Applying the transformation on the radial metric function leads these equations to two distinct sets, each representing the influence of either the seed or additional source exclusively. In order to formulate the black hole solutions, the seed source is considered to be a vacuum, characterized by the Schwarzschild metric. To derive a viable solution for the second system, constraints are imposed on the metric potentials and energy-momentum tensor of the additional source. Three distinct solutions are graphically analyzed based on varying values of the decoupling parameter. The energy conditions are also plotted to determine the nature of the extra source. Finally, it is concluded that two of our three developed models agree with the asymptotic flatness criterion and energy bounds in this modified theory.