In this paper, we study the viability and stability of anisotropic compact
stars in the context of $f(mathcal{Q})$ theory, where $mathcal{Q}$ is
non-metricity scalar. We use Finch-Skea solutions to investigate the physical
properties of compact stars. To determine the values of unknown constants, we
match internal spacetime with the exterior region at the boundary surface.
Furthermore, we study the various physical quantities, including effective
matter variables, energy conditions and equation of state parameters inside the
considered compact stars. The equilibrium and stability states of the proposed
compact stars are examined through the Tolman-Oppenheimer-Volkoff equation,
causality condition, Herrera cracking approach and adiabatic index,
respectively. It is found that viable and stable compact stars exist in
$f(mathcal{Q})$ theory as all the necessary conditions are satisfied.
In this paper, the viability and stability of anisotropic compact stars in the context of $f(mathcal{Q})$ theory are studied. The main objective is to determine whether compact stars can exist in this theory and whether they are stable. To investigate this, Finch-Skea solutions are used to understand the physical properties of compact stars.
To determine the values of unknown constants, the internal spacetime is matched with the exterior region at the boundary surface. This ensures that the compact star is in equilibrium with its surroundings. Various physical quantities, including effective matter variables, energy conditions, and equation of state parameters, are studied inside the compact star to understand its behavior.
The equilibrium and stability states of the proposed compact stars are examined through multiple approaches. The Tolman-Oppenheimer-Volkoff equation is used to determine if the compact star is in equilibrium. The causality condition ensures that no physical signals propagate faster than the speed of light within the star. The Herrera cracking approach checks for potential instabilities caused by pressure exerted on the boundary of the star. Finally, the adiabatic index is used to assess the stability of the compact star.
The conclusions of this study indicate that viable and stable compact stars can exist in $f(mathcal{Q})$ theory. All necessary conditions for viability and stability are satisfied. This opens up new possibilities for understanding compact stars in alternative theories of gravity.
Roadmap for Readers
- Introduction: Provides an overview of the study and the motivation behind it.
- Methodology: Explains the approach taken to investigate the viability and stability of compact stars in $f(mathcal{Q})$ theory, including the use of Finch-Skea solutions and matching internal spacetime with the exterior region.
- Physical Properties: Discusses the various physical quantities studied inside the compact star, such as effective matter variables, energy conditions, and equation of state parameters.
- Equilibrium and Stability: Describes the methods used to examine the equilibrium and stability states of the proposed compact stars, including the Tolman-Oppenheimer-Volkoff equation, causality condition, Herrera cracking approach, and adiabatic index.
- Conclusions: Summarizes the findings of the study, indicating that viable and stable compact stars exist in $f(mathcal{Q})$ theory.
Potential Challenges and Opportunities
- Challenge: Further research is needed to explore the physical implications and observational consequences of compact stars in $f(mathcal{Q})$ theory. This could involve studying their gravitational wave signatures or investigating their role in astrophysical phenomena.
- Opportunity: The existence of viable and stable compact stars in $f(mathcal{Q})$ theory suggests that alternative theories of gravity can provide new insights into the nature of these astrophysical objects. This opens up avenues for future research and expands our understanding of compact stars beyond traditional theories.
Overall, this study contributes to the growing field of alternative theories of gravity and highlights the potential existence of compact stars in $f(mathcal{Q})$ theory. Further exploration of this topic will deepen our understanding of compact stars and their role in the universe.