“Anisotropic Interior Solutions in $f(G,T)$ Gravity: Stability and Viability Analysis”

arXiv:2406.01632v1 Announce Type: new
Abstract: In this paper, we investigate the anisotropic interior spherically symmetric solutions by utilizing the extended gravitational decoupling method in the background of $f(G,T)$ gravity, where $G$ and $T$ signify the Gauss-Bonnet term and trace of the stress-energy tensor, respectively. The anisotropy in the interior geometry arises with the inclusion of an additional source in the isotropic configuration. In this technique, the temporal and radial potentials are decoupled which split the field equations into two independent sets. Both sets individually represent the isotropic and anisotropic configurations, respectively. The solution corresponding to the first set is determined by using the Krori-Barua metric potentials whereas the second set contains unknown which are solved with the help of some constraints. The ultimate anisotropic results are evaluated by combining the solutions of both distributions. The influence of decoupling parameter is examined on the matter variables as well as anisotropic factor. We illustrate the viable and stable features of the constructed solutions by using energy constraints and three stability criteria, respectively. Finally, we conclude that the obtained solutions are viable as well as stable for the whole domain of the coupling parameter.

Article Title: Investigating Anisotropic Interior Spherically Symmetric Solutions in $f(G,T)$ Gravity

Introduction

In this paper, the authors explore anisotropic interior spherically symmetric solutions in the framework of $f(G,T)$ gravity. By utilizing the extended gravitational decoupling method, the authors aim to understand the influence of a decoupling parameter on the matter variables and anisotropic factor. This investigation provides insights into the viability and stability of the constructed solutions.

Methodology

The extended gravitational decoupling method is employed to study the anisotropic interior geometry in $f(G,T)$ gravity. By decoupling the temporal and radial potentials, the field equations are split into two independent sets. The first set represents the isotropic configuration and is determined using the Krori-Barua metric potentials. The second set, which corresponds to the anisotropic configuration, contains unknowns that are solved with the help of constraints.

Results

The authors obtain anisotropic results by combining the solutions of both distributions. They evaluate the influence of the decoupling parameter on the matter variables and anisotropic factor. The viability of the solutions is illustrated using energy constraints, while three stability criteria are employed to assess their stability.

Conclusion

The authors conclude that the obtained solutions in $f(G,T)$ gravity are both viable and stable across the entire domain of the coupling parameter. These findings contribute to the understanding of anisotropic interior spherically symmetric solutions and have potential implications for future studies in this field.

Roadmap for Readers:

1. Introduction to anisotropic interior spherically symmetric solutions in $f(G,T)$ gravity
2. Overview of the extended gravitational decoupling method
3. Explanation of the field equations and their decoupling into two independent sets
4. Solution determination for the isotropic configuration using Krori-Barua metric potentials
5. Solution determination for the anisotropic configuration with the help of constraints
6. Combining the solutions to obtain anisotropic results
7. Analysis of the influence of the decoupling parameter on matter variables and anisotropic factor
8. Evaluation of viability using energy constraints
9. Assessment of stability using three stability criteria
10. Conclusion on the viability and stability of the solutions in the whole domain of the coupling parameter

Potential Challenges:

• Complex mathematical equations and concepts may require a strong understanding of theoretical physics.
• The extended gravitational decoupling method may be unfamiliar to readers, necessitating additional background research.
• The constraints used to solve for the unknowns in the anisotropic configuration may present computational challenges.
• The evaluation of viability and stability criteria may involve intricate calculations.

Potential Opportunities:

• This paper contributes to the field of anisotropic interior spherically symmetric solutions in $f(G,T)$ gravity, providing a potential avenue for further research and exploration.
• Readers can gain insights into the decoupling method and its application in gravitational physics.
• The obtained solutions’ viability and stability can inspire future investigations in related areas.
• The influence of the decoupling parameter on matter variables and anisotropic factor opens avenues for expanding the understanding of these variables.

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