# Models of Collapsing and Expanding Anisotropic Gravitating Source in $f(R,T)$ Theory of Gravity

## TL;DR

This paper derives exact solutions for non-static anisotropic gravitating sources in $f(R,T)$ gravity, analyzing conditions for expansion and collapse, and exploring the effects of the coupling parameter on physical properties.

## Contribution

It provides new parametric solutions in $f(R,T)$ gravity for anisotropic fluids, examining expansion, collapse, and horizon conditions with detailed analysis of the coupling parameter's impact.

## Key findings

- Existence of a single horizon in the model
- Conditions for expansion and collapse based on parameters
- Graphical analysis of energy density and pressures

## Abstract

In this paper, we have formulated the exact solutions of the non-static anisotropic gravitating source in $f(R,T)$ gravity which may lead to expansion and collapse. By assuming the no thermal conduction in gravitating source, we have determine parametric solutions in $f(R,T)$ gravity with non-static spherical geometry filled with anisotropic fluid. We have examined the range of parameter for which expansion scalar become negative and positive leading to collapse and expansion, respectively. Further, using the definition of mass function the condition for the trapped surface have been explored and it has been investigated there exists a single horizon in this case. The impact of coupling parameter $\lambda$ has been discussed in detail in both cases. For the various values of coupling parameter $\lambda$, we have plotted energy density, anisotropic pressure and anisotropic parameter in case of collapse and expansion. The physical significance of the graphs has been explained in detail.