This paper presents the study of dark-energy compact stars in the context of
modified Rastall teleparallel gravity. It is the first time that dark energy
celestial phenomena have been explored in this modified gravitational theory.
Employing the torsion-based functions, $f(T)$ and $h(T)$, we analyzed their
effects in a spherically symmetric spacetime chosen as the interior geometry,
while using the Schwarzschild geometry as an outer spacetime. In this study, we
explored various dark energy stellar properties, including dark energy pressure
components, energy conditions, and equation of state components. Our findings
reveal that the observed negative behavior of these stellar properties served
as compelling evidence, validating the presence of dark energy in stellar
configurations. Detailed investigations of the energy conditions, pressure
profiles, sound speeds, TOV equation, adiabatic index, gradients, mass
function, compactness, and redshift function forecasts a comprehensive
assessment, affirming the acceptability and realism of the investigated stellar
configuration.
Conclusion
The study presented in this paper explores the concept of dark-energy compact stars within the framework of modified Rastall teleparallel gravity. This is the first investigation of dark energy in stellar configurations using this modified gravitational theory. By analyzing the effects of torsion-based functions in a spherically symmetric interior geometry and Schwarzschild exterior geometry, various properties of dark energy in stellar objects were examined.
Our findings indicate that the negative behavior of dark energy pressure components, energy conditions, and equation of state components provide strong evidence for the existence of dark energy in stellar configurations. In-depth investigations of additional properties such as pressure profiles, sound speeds, TOV equation, adiabatic index, gradients, mass function, compactness, and redshift function further support the acceptability and realism of the studied stellar configuration.
Roadmap for Readers
To further understand and explore the implications of this study and its potential impact, the following roadmap is provided:
1. Further Analysis of Energy Conditions
- Investigate the energy conditions in different dark-energy compact stars to identify any variations or patterns.
- Compare the results with known theories and experimental data to validate the findings.
- Explore the implications of different energy conditions on the stability and behavior of dark-energy compact stars.
2. Study of Pressure Profiles and Sound Speeds
- Analyze the pressure profiles and sound speeds in different dark-energy compact stars to understand their relationship with the presence of dark energy.
- Examine how variations in pressure profiles and sound speeds affect the overall structure and dynamics of these stellar configurations.
3. Investigation of TOV Equation and Adiabatic Index
- Explore how the Tolman-Oppenheimer-Volkoff (TOV) equation is affected by the presence of dark energy in compact stars.
- Examine the behavior of the adiabatic index in different dark-energy compact stars and its impact on their stability.
4. Study of Gradients and Mass Function
- Analyze the gradients and mass function in dark-energy compact stars to understand their relationship with the distribution and concentration of dark energy within these objects.
- Investigate how the mass function is affected by variations in dark energy properties and its implications for the overall structure of compact stars.
5. Assessment of Compactness and Redshift Function
- Examine the compactness of dark-energy compact stars and its relationship with the presence of dark energy.
- Analyze the redshift function to understand how dark energy contributes to the observed redshift in stellar objects.
Challenges and Opportunities on the Horizon
While this study provides valuable insights into dark-energy compact stars, several challenges and opportunities lie ahead:
Challenge: The complexity of modified Rastall teleparallel gravity and its implications for studying dark-energy compact stars may require advanced theoretical frameworks and mathematical tools.
Opportunity: Further developments in theoretical physics and mathematical modeling can enhance our understanding of the modified gravitational theory and its applications.
Challenge: Experimentally confirming the existence and properties of dark-energy compact stars may pose significant challenges due to the current limitations of observational techniques.
Opportunity: Advancements in observational technologies and techniques can provide new insights into dark-energy phenomena in stellar configurations.
Challenge: Validating the acceptability and realism of dark-energy compact stars requires a comprehensive assessment encompassing a wide range of properties and conditions.
Opportunity: Collaborative efforts between researchers from multiple disciplines can facilitate a holistic examination of these stellar configurations and provide a more comprehensive understanding of their nature.
By addressing these challenges and embracing the opportunities, future research in the field of dark-energy compact stars can shed light on the fundamental nature of dark energy and its role in the cosmos.