Universality and Breakdown of Universality in Critical Gravitational Collapse of a Complex Scalar Field

מושגי ליבה

This research paper investigates the critical gravitational collapse of a massless complex scalar field in axisymmetry, revealing that while the spherical case exhibits universality similar to the real scalar field, deviations from spherical symmetry lead to a breakdown of universality, potentially driven by gravitational waves.

תקציר

• Bibliographic Information: Marouda, K., Cors, D., Rüter, H.R., Atteneder, F., & Hilditch, D. (2024). Twist-free axisymmetric critical collapse of a complex scalar field. arXiv preprint arXiv:2402.06724v2.
• Research Objective: This study aims to explore the critical behavior of a massless complex scalar field minimally coupled to general relativity in axisymmetry, focusing on deviations from spherical symmetry and their impact on the universality of the critical solution.
• Methodology: The authors employ the pseudospectral code bamps to perform numerical simulations of the Einstein-Klein-Gordon system, using a DSS-compatible gauge and hp-adaptive mesh refinement to resolve the dynamics near the threshold of black hole formation. They investigate a neighborhood of the spherically symmetric critical solution in phase space, considering initial data with varying degrees of asphericity.
• Key Findings:
  • In spherical symmetry, the complex scalar field exhibits critical behavior analogous to the real scalar field, with a universal critical solution and characteristic scaling laws.
  • As asphericity increases, the authors observe a drift in the scaling exponents and echoing periods, indicating a breakdown of universality.
  • For sufficiently large asphericities, the center of collapse bifurcates on the symmetry axis, suggesting that gravitational waves may drive the collapse in this regime.
• Main Conclusions: The study provides evidence that the universality observed in spherical symmetry for critical gravitational collapse does not necessarily extend to less symmetric scenarios. The breakdown of universality in the complex scalar field case, similar to previous findings for vacuum collapse, suggests a more intricate picture of critical phenomena in general relativity.
• Significance: This research contributes to the understanding of critical phenomena in gravitational collapse, particularly in the context of axisymmetric spacetimes. The findings have implications for the study of black hole formation and the validity of the cosmic censorship conjecture.
• Limitations and Future Research: The study is limited by computational resources, which restrict the degree of tuning to the threshold of collapse. Future research could explore the use of higher-order methods or alternative formulations of general relativity to improve the accuracy of the simulations. Additionally, investigating the role of angular momentum and the transition to different symmetry classes could provide further insights into the nature of critical collapse.

סטטיסטיקה

For the spherical case, the echoing period is found to be ∆ = 3.43 ± 0.03, consistent with the value for the real scalar field.
The scaling exponent γ for subcritical runs is approximately 0.37, aligning with the established value for the real scalar field in spherical symmetry.

ציטוטים

"In this study, we explore gravitational collapse involving a massless complex scalar field minimally coupled to general relativity."
"We employ the pseudospectral code bamps to investigate a neighborhood of the spherically symmetric critical solution in phase space, focusing on aspherical departures from it."
"At sufficiently high asphericities we find that the center of collapse bifurcates, on the symmetry axis, but away from the origin."
"Finally we look for and evaluate evidence that in the highly aspherical setting the collapse is driven by gravitational waves."

תובנות מפתח מזוקקות מ:

Twist-free axisymmetric critical collapse of a complex scalar field

by Krin... ב- arxiv.org 10-18-2024

https://arxiv.org/pdf/2402.06724.pdf

שאלות מעמיקות

How does the presence of angular momentum affect the critical behavior and universality of the complex scalar field collapse?

The provided text focuses on twist-free, axisymmetric collapse of a complex scalar field, which inherently implies zero angular momentum. Therefore, the text doesn't directly address the impact of angular momentum on critical behavior. However, we can discuss the potential effects based on existing literature:

Breaking of Spherical Symmetry: Angular momentum would further break the symmetry of the system. While the text explores deviations from spherical symmetry within the axisymmetric limit, introducing angular momentum would lead to a more complex, fully three-dimensional collapse scenario.

New Critical Solutions: It's highly probable that angular momentum would give rise to new families of critical solutions, distinct from those observed in spherically symmetric or twist-free axisymmetric cases. These solutions might exhibit different echoing periods (Δ), scaling exponents (γ), and potentially new forms of self-similarity.

Impact on Universality: The text already highlights challenges to universality in the twist-free axisymmetric case. Angular momentum would likely amplify these challenges. The specific form and properties of the critical solutions would likely depend on the initial angular momentum profile, potentially leading to a richer, but less universal, landscape of critical behavior.

Reference to Existing Work: The text mentions a study ([22]) that investigated massless complex scalar field collapse with angular momentum in axisymmetry. This study found critical solutions with distinct echoing periods and scaling exponents compared to the real scalar field case. This finding suggests that angular momentum can indeed significantly alter the critical behavior.

Could the observed breakdown of universality be an artifact of the numerical simulations, or does it reflect a genuine feature of the Einstein-Klein-Gordon system?

The text raises a crucial question about the observed deviations from universality in axisymmetric collapse: are these deviations genuine features of the Einstein-Klein-Gordon system, or are they artifacts of the numerical simulations?
Arguments for a Genuine Feature:

Consistency Across Studies: The text mentions that three independent research groups ([14]) found consistent evidence for the breakdown of universality in twist-free axisymmetric vacuum collapse. This agreement across different numerical codes and approaches strengthens the argument for a genuine physical effect.
Qualitative Differences: The observed deviations, such as the dependence of the scaling exponents and collapse locations on initial data families, represent qualitative departures from the universal behavior observed in spherical symmetry. This suggests a fundamental shift in the dynamics of critical collapse.
Theoretical Insights: Theoretical studies, like the perturbative analysis by Martín-García & Gundlach ([21]), provide some theoretical grounding for the potential breakdown of universality. Their work suggests that aspherical perturbations can grow in certain scenarios, leading to non-universal behavior.
Arguments for Potential Numerical Artifacts:

Limitations of Numerical Simulations: Numerical relativity simulations are inherently limited by factors like finite resolution, numerical errors, and gauge choices. These limitations could potentially introduce spurious effects that might be misinterpreted as a breakdown of universality.
Difficulty in Approaching Criticality: Accurately simulating critical collapse requires extremely high resolutions and fine-tuning of initial data. Even small numerical errors can significantly impact the observed behavior near the threshold of collapse.
Need for Further Investigation: The text acknowledges the need for more robust and reliable numerical tools, such as improved apparent horizon finders, to conclusively rule out numerical artifacts.
Conclusion:
While the evidence suggests that the breakdown of universality might reflect a genuine feature of the Einstein-Klein-Gordon system, it's crucial to acknowledge the inherent limitations of numerical simulations. Further investigation with improved numerical techniques and more detailed theoretical analysis is essential to definitively answer this question.

What are the implications of these findings for our understanding of the cosmic censorship conjecture and the formation of naked singularities?

The findings presented in the text, particularly the potential breakdown of universality in axisymmetric collapse, have intriguing implications for our understanding of the cosmic censorship conjecture and the formation of naked singularities:

Challenging the Genericity of Criticality: The cosmic censorship conjecture posits that singularities formed in gravitational collapse are generically hidden within black holes, preventing their observation from the outside universe. Critical phenomena, with their fine-tuned initial conditions, are often considered as potential counter-examples. However, if universality breaks down in more general, less symmetric scenarios, it suggests that critical behavior might be less generic than previously thought, potentially strengthening the case for cosmic censorship.

New Pathways to Naked Singularities: On the other hand, the breakdown of universality and the emergence of diverse critical solutions could imply the existence of new pathways for forming naked singularities. If the specific form of the critical solution and its stability properties depend sensitively on the initial conditions, it might open up possibilities for scenarios where naked singularities could form under more generic circumstances.

Rethinking the Role of Symmetry: The observed differences between spherical and axisymmetric collapse highlight the crucial role of symmetry in shaping critical behavior. The breakdown of universality in less symmetric cases suggests that the idealized picture obtained in spherical symmetry might not fully capture the complexity of gravitational collapse in more realistic astrophysical settings.

Further Research Directions: These findings motivate further research into the following areas:

Exploring Collapse in Full 3D: Investigating critical phenomena in fully three-dimensional simulations without any symmetry assumptions is crucial to understanding the generality of these findings.
Analyzing the Stability of Critical Solutions: Determining the stability properties of the diverse critical solutions found in axisymmetric and 3D collapse is essential to assess their potential relevance to astrophysical scenarios.
Developing Theoretical Frameworks: Formulating robust theoretical frameworks that can describe critical behavior beyond spherical symmetry is crucial for a deeper understanding of the underlying physics.
Conclusion:
The potential breakdown of universality in axisymmetric collapse presents both challenges and opportunities for our understanding of cosmic censorship and naked singularities. While it might strengthen the case for cosmic censorship by suggesting that critical behavior is less generic, it also opens up new possibilities for forming naked singularities through diverse critical solutions. Further research is essential to unravel the full implications of these findings and their impact on our understanding of gravity's most extreme phenomena.