Stellar structure models in modified theories of gravity: lessons and challenges (1912.05202v2)

Abstract: The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of the strong field regime of General Relativity, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its principles. These theories typically change the stellar structure equations, thus having a large impact on the astrophysical properties of the corresponding stars and opening a new window to constrain these theories with present and future observations. For relativistic (neutron) stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters of the modified gravity side, providing new phenomenology for the predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars (white, brown and red dwarfs), the weakening/strengthening of the gravitational force inside astrophysical bodies may induce changes on the star's mass, radius or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning in brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modellings, and observational aspects, highlighting some of the most promising opportunities in the field.

• The paper refines TOV equations and introduces new equations of state to model mass-radius relations in stars under modified gravity.
• It applies these modified frameworks to both relativistic stars like neutron stars and non-relativistic stars, affecting compactness and luminosity.
• The study establishes practical constraints on gravitational parameters that reconcile observational data with theoretical predictions in extreme environments.

Stellar Structure Models in Modified Theories of Gravity

Overview

In the paper titled "Stellar Structure Models in Modified Theories of Gravity: Lessons and Challenges," the authors explore the complexities of understanding stellar structures through the lens of modified gravity theories. This research addresses both relativistic stars, like neutron stars, which exhibit extreme conditions not covered by General Relativity (GR), and non-relativistic stars, such as white, brown, and red dwarfs. The paper proposes that these astrophysical objects serve as unique laboratories to test and constrain modified gravity theories and highlights the impact such theories have on nuclear force estimations and gravitational interactions at high intensity.

Key Insights and Results

1. Spherical Symmetry: The paper covers various modifications of the Einstein-Hilbert action, specifically through $f(R)$ gravity and its extensions. This approach results in changes to the Tolman-Oppenheimer-Volkoff (TOV) equations and necessitates novel equations of state (EOS) to account for phenomena like mass-radius configurations and maximum mass predictions.
2. Modified Gravity and Observations: For relativistic stars, particularly neutron stars, the modified theories introduce parameters resulting in predictions that remain consistent with observational constraints such as mass measurement at the 2 solar mass threshold. These parameters affect the compactness, radius, and maximum mass predictions, and can potentially alleviate the hyperon puzzle by adjusting softness in EOS.
3. Non-relativistic Stars: For non-relativistic stars, modifications influence the gravitational equilibrium leading to altered mass-radius relations and luminosity changes. The Lane-Emden equation is used to provide insights for these stellar structures, including potential impacts on Chandrasekhar's limit and the determination of minimum mass necessary for stable hydrogen burning.
4. Theoretical Implications: The research identifies limitations inherent to GR and provides thorough exploration of the sphere surface boundary conditions essential for stable star configurations. This emphasizes how modified gravity theories could enhance predictions of stellar behaviors under circumstances that GR approaches fail to accurately describe.

Implications and Future Developments

The implications of understanding stellar structures through modified gravity go beyond astrophysics, affecting how cosmic phenomena are viewed and potentially resolving existing disparities between theoretical predictions and observed data. Practical implications include redefining constraints on gravitational theory fundamentals, enhancing predictions of stellar evolution and behaviors, and providing new parameters for computational models in cosmology.

The authors speculate that the synergy between theoretical computation and observational data collection can substantially refine models of stellar mechanics under modified gravity theories, giving rise to more predictive power and insights into cosmic structures beyond current capabilities. Revitalizing interest in modified gravity theories, this research suggests a promising avenue to reconcile observational discrepancies and gain deeper insights into physical processes in extreme environments.

In conclusion, this paper offers a comprehensive insight into how modified theories of gravity can impact and challenge our understanding of stellar structures, presenting both the challenges and the lessons learned from integrating modified gravitational dynamics with astrophysical observations. As developments in AI and computational physics advance, these theories are expected to flourish, notably in areas concerning the synthesis of observational data and theoretical frameworks.