This paper discusses the gravitational collapse of dynamical self-gravitating

fluid distribution in $f(mathcal{R},mathcal{T},mathcal{Q})$ gravity, where

$mathcal{Q}=mathcal{R}_{varphivartheta}mathcal{T}^{varphivartheta}$. In

this regard, we assume a charged anisotropic spherical geometry involving

dissipation flux and adopt standard model of the form

$mathcal{R}+Phisqrt{mathcal{T}}+Psimathcal{Q}$, where $Phi$ and $Psi$

symbolize real-valued coupling parameters. The Misner-Sharp as well as

M”{u}ler-Israel Stewart mechanisms are employed to formulate the corresponding

dynamical and transport equations. We then interlink these evolution equations

which help to study the impact of state variables, heat dissipation, modified

corrections and charge on the collapse rate. The Weyl scalar is further

expressed in terms of the modified field equations. The necessary and

sufficient condition of conformal flatness of the considered configuration and

homogeneous energy density is obtained by applying some constraints on the

model along with disappearing charge and anisotropy. Finally, we discuss

different cases to investigate how the spherical matter source is affected by

the charge and modified corrections.

This paper explores the gravitational collapse of a dynamical self-gravitating fluid distribution in $f(mathcal{R},mathcal{T},mathcal{Q})$ gravity, where $mathcal{Q}=mathcal{R}_{varphivartheta}mathcal{T}^{varphivartheta}$. The study focuses on a charged anisotropic spherical geometry with dissipation flux, utilizing the standard model $mathcal{R}+Phisqrt{mathcal{T}}+Psimathcal{Q}$, where $Phi$ and $Psi$ are real-valued coupling parameters.

To formulate the dynamical and transport equations, the Misner-Sharp and M”{u}ler-Israel Stewart mechanisms are employed. The evolution equations are then interconnected to examine the impact of state variables, heat dissipation, modified corrections, and charge on the collapse rate. Additionally, the Weyl scalar is expressed in terms of the modified field equations.

The paper also derives the necessary and sufficient condition for conformal flatness of the considered configuration and homogeneous energy density by applying constraints on the model, including the absence of charge and anisotropy.

Lastly, the study explores various cases to investigate how the charge and modified corrections affect the spherical matter source.

## Roadmap: Challenges and Opportunities

- Further research is needed to explore the implications of $f(mathcal{R},mathcal{T},mathcal{Q})$ gravity on other astrophysical phenomena.
- Understanding the behavior of the collapse rate under different conditions and parameters can provide insights into the dynamics of gravitational collapse.
- The study opens up opportunities to investigate the effects of charge and modified corrections on other properties of gravitating systems.
- Exploring the interplay between dissipation flux and the dynamical and transport equations can uncover new insights on the behavior of self-gravitating fluids.
- Further analysis of the conformal flatness condition and its implications for other physical systems could lead to new understanding of geometric properties.

## Conclusion

This paper presents a comprehensive study on the gravitational collapse of a dynamical self-gravitating fluid distribution in $f(mathcal{R},mathcal{T},mathcal{Q})$ gravity. By incorporating a charged anisotropic spherical geometry with dissipation flux, the impact of state variables, heat dissipation, modified corrections, and charge on the collapse rate is examined. The necessary and sufficient condition for conformal flatness of the system is derived, along with analyses of different cases considering the effects of charge and modified corrections. This research contributes to our understanding of gravitational collapse in alternative gravity theories and opens up opportunities for further exploration and investigation in the field.