Rotating Stars in Relativity (1612.03050v2)

Abstract: Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in $f$-modes and $r$-modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.

Rotating Stars in Relativity: An Overview

The paper "Rotating Stars in Relativity" by Vasileios Paschalidis and Nikolaos Stergioulas presents an extensive review of the theoretical and numerical understanding of rotating relativistic stars. These celestial bodies are significant for understanding the equation of state (EOS) at high densities and serve as potential sources of gravitational waves.

Key Contributions and Findings

1. Updated Theoretical and Observational Insights:

• The paper provides an update on equilibrium properties, oscillations, and instabilities, focusing on $f$-modes and $r$-modes.
• It discusses rotating star scenarios in both standard and modified gravitational theories, equilibrium configurations in low-mass X-ray binaries (LMXBs), and examines rotating strange stars.

2. Numerical Methods and Modelling:

• Various numerical techniques for solving equilibrium configurations in full general relativity are detailed, including the successes of multiple domain spectral methods.
• The comparison between different computational codes highlights discrepancies and advancements in modelling accuracy.

3. Astrophysical Implications:

• The impact of rotation on neutron stars' maximum mass and stability was explored, noting that rotation generally increases the mass a star can sustain.
• The paper also examines the secular and dynamical instabilities in rotating stars, emphasizing relativistic stars' enhanced susceptibility to these instabilities compared to Newtonian stars.

Numerical Results and Strong Claims

The numerical studies presented show that:

• Relativistic rotation can extend the maximum mass limit of neutron stars by 15-20% over non-rotating models.
• Rotating models exhibit different instability thresholds compared to their non-rotating counterparts.

Implications for Future Research

1. Gravitational Wave Astronomy:

• The insights into rotating stars have implications for gravitational wave detections. As demonstrated by LIGO and Virgo, understanding the precise mechanisms of rotating stars can refine detections and interpretations of gravitational wave signals.

2. Neutron Star Equation of State:

• By linking rotation rates to observable properties such as mass and radius, the paper provides a framework for constraining the EOS for nucleonic matter at high densities, thus contributing to a better understanding of neutron star interiors.

3. Modified Theories of Gravity:

• The research includes exploratory studies into rotating stars within the framework of modified gravity theories, paving the way for evaluating these theories' robustness and implications on astrophysical phenomena.

Future Developments in AI and Simulations

AI-driven models could enhance the precision of simulations of rotating neutron stars by providing more efficient algorithms for resolving complex equations of state and gravitational models. Machine learning techniques might reduce computational costs, streamline parameter exploration, and refine waveform predictions in gravitational wave astronomy.

Overall, the paper offers a comprehensive review, inviting future exploration into the myriad unknowns surrounding rotating stars' behavior and characteristics. The work underscores the importance of both theoretical and numerical advancements for improving our understanding of neutron stars and their role in the universe.