arXiv:2502.05217v1 Announce Type: new
Abstract: In this paper, we consider the spherically symmetric gravitational collapse of isotropic matter undergoing dissipation in the form of heat flux, with a generalized Vaidya exterior, in the context of $f(R, T)$ gravity. Choosing $f(R, T)=R+2lambda T$, and applying the $f(R, T)$ junction conditions on the field equations for the interior and exterior regions, we have obtained matching conditions of the matter-Lagrangian and its derivatives across the boundary. The time of formation of singularity and the time of formation of apparent horizon have been determined and constraints on the integration constants are examined for which the final singularity is hidden behind the horizon.
In this paper, the authors study the gravitational collapse of isotropic matter with dissipation in the form of heat flux, using the framework of $f(R, T)$ gravity. They focus on the spherically symmetric case, with a generalized Vaidya exterior. The specific choice for the $f(R, T)$ function is $f(R, T)=R+2lambda T$, and the authors apply the $f(R, T)$ junction conditions to the field equations for the interior and exterior regions.
One of the main results of the study is the matching conditions of the matter-Lagrangian and its derivatives across the boundary. These matching conditions are important for a consistent description of the gravitational collapse process.
The authors then determine the time of formation of the singularity and the time of formation of the apparent horizon. They examine the constraints on the integration constants that lead to the singularity being hidden behind the horizon.
Roadmap for Readers
To further explore the topic of spherically symmetric gravitational collapse and its relation to $f(R, T)$ gravity, readers can follow the suggested roadmap:
1. Understand the basics of gravitational collapse
Before diving into the specific case of spherically symmetric collapse, it is important to have a solid understanding of the basics of gravitational collapse. Readers should familiarize themselves with concepts such as singularities, event horizons, and the different types of collapse scenarios.
2. Study the Vaidya metric and its application to gravitational collapse
The Vaidya metric is a useful tool for describing the gravitational collapse process. Readers should study the properties of the Vaidya metric and its application to modeling collapse scenarios. This will provide the necessary background for understanding the specific case considered in the paper.
3. Learn about $f(R, T)$ gravity
$f(R, T)$ gravity is a modified theory of gravity that includes additional terms in the gravitational action. Readers should familiarize themselves with the basic concepts of $f(R, T)$ gravity and its motivations. Understanding the field equations and the junction conditions will be crucial for comprehending the results presented in the paper.
4. Analyze the matching conditions derived in the paper
The matching conditions of the matter-Lagrangian and its derivatives across the boundary are an essential result of the study. Readers should carefully analyze these matching conditions and understand their implications for the physical description of the collapse process.
5. Explore the constraints on integration constants
The constraints on the integration constants, which determine whether the singularity is hidden behind the horizon, are an important aspect of the study. Readers should investigate the different constraints and their implications. This will provide insights into the behavior of collapsing systems in $f(R, T)$ gravity.
6. Consider other applications and extensions
Finally, readers can consider other applications and extensions of the results presented in the paper. This could include studying different matter models, exploring alternative $f(R, T)$ functions, or investigating the implications for black hole formation.
Challenges and Opportunities
While studying the spherically symmetric collapse in the context of $f(R, T)$ gravity opens up new avenues of research, several challenges and opportunities lie ahead:
- Theoretical Challenges: The theoretical analysis of gravitational collapse in modified gravity theories is a challenging task. Readers should be prepared to delve into advanced mathematical techniques and field equations.
- Experimental Verification: The predictions of $f(R, T)$ gravity for gravitational collapse need to be tested against observational data or laboratory experiments. The opportunities for experimental verification can lead to a deeper understanding of the theory.
- Extensions and Generalizations: The results obtained in this paper are specific to spherically symmetric collapse with a particular $f(R, T)$ function. Readers can explore extensions of the study to other geometries, matter models, or different choices of $f(R, T)$ functions.
- Connections to Other Fields: Gravitational collapse has connections to various fields, such as astrophysics and cosmology. Readers can explore the interdisciplinary aspects and implications of the results in this paper.
In summary, readers interested in the spherically symmetric gravitational collapse and its relation to $f(R, T)$ gravity should follow a roadmap that includes understanding the basics, studying the specific case presented in the paper, analyzing the derived matching conditions and constraints, and exploring further applications and extensions. Along the way, they will encounter theoretical challenges, opportunities for experimental verification, possibilities for generalizations, and connections to other fields.