We present the complete system of equations and matching conditions describing a physically meaningful, charged spherically symmetric gravitational collapse within the framework of f(R,Lm,T) gravity. By employing the Israel-Stewart formalism, we examine the collapse dynamics of a fluid undergoing viscous dissipation, i.e., the standard Misner–Sharp formulation for spherical collapse, originally developed for perfect fluids, is generalized to incorporate three dissipative channels: heat conduction, shear viscosity, and bulk viscosity. Two distinct physical regimes are adopted to handle dissipative fluxes. The first is the streaming-out approximation, valid when the system size is much smaller than a particle’s mean free path. The second is the diffusion approximation, appropriate for optically thick media where flux generation arises from spatial gradients. After deriving the dynamical equation, we contrast our findings with earlier studies that omitted the above parameters and disregarded dissipative flow variables. A key aspect of our analysis is an investigation into how electric charge modifies the relationship between the Weyl tensor and energy density non-uniformity, which we integrate appropriately into the broader context of dissipative collapse. Our results may hold relevance under specific astrophysical conditions.
This article examines how the early universe evolved by studying the perturbation behavior in the context of f(R,Lm) gravity. We analyze various cosmological stages, including the sub-relativistic, radiation-dominated, ultra-relativistic, dust, and stiff fluid universe, using methods including power-law scale factor techniques. We also probe bouncing cosmological solutions in f(R,Lm) gravity, focusing on reconstructing gravitational Lagrangians that fit specific parameter constraints. By using these derived Lagrangians, we delve into the energy conditions required for successful Galileon bounce scenarios. Our research emphasizes the role of exotic matter, which, with its strong negative pressure, drives the accelerated expansion of the universe. By exploring f(R,Lm) gravity theories and their related bouncing scenarios, which help develop in understanding of cosmological dynamics, distinguish our work from earlier studies on other gravity theories and their effects on the universe’s evolution.
This manuscript deals with exploring the exact soliton solutions of a truncated M-fractional Kraenkel-Manna-Merle system by using the Sardar sub-equation method and the unified method. It is important to note that the KMM system plays a crucial role as a mathematical model of coupled nonlinear wave propagation and magnetization processes in ferromagnetic and ferrite materials. A broad spectrum of analytical solutions to the FKMM system is given by hyperbolic function, trigonometric function solutions, rational function solutions, and exponential function solutions with a wide range of different nonlinear profiles of bright solitons, dark solitons, singularity solutions, periodic solutions, kink solitons, kink-bright solitons, and peakon solutions. We also explore how changing the fractional order affects these shapes by comparing graphs with different values. In addition to theoretical derivations, the study includes stability analysis for the derived solutions. Furthermore, we investigate bifurcation analysis in which the transformation transformed the system into a planar dynamical system, allowing phase portraits to be examined. To aid in visual comprehension of the solutions, 3D, 2D, and contour graphs of the executed solutions are also provided. This is useful for solving a number of nonlinear equations that can be found in different areas of science, such as fluid dynamics, propagation of information in optical fibers, plasma physics, ocean engineering, dynamics of time-dependent systems, and solid-state physics. This reliable, important, and efficient approach can be applied to solve a number of additional physics and other applied science models. All results are tested using computational simulations in Mathematica and MATLAB, ensuring their precision and consistency.
