Critical phenomena in gravitational collapse are characterized by the emergence of surprising structure in solution space, namely the appearance of universal power-laws and periodicities near the threshold of collapse, and a universal discretely self-similar solution at the threshold itself. This seminal work spurred a comprehensive investigation of extreme spherical spacetimes in numerical relativity, with analogous results for numerous matter models. Recent research suggests that the generalization to less symmetric scenarios is subtle. In twist-free axisymmetric vacuum collapse for instance, numerical evidence suggests a breakdown of universality of solutions at the threshold of collapse. 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. First, working in explicit spherical symmetry, we find strong evidence that the spacetime metric of the spherical critical solution of the complex scalar field agrees with that of the Choptuik solution. We then examine universality of the behavior of solutions near the threshold of collapse as the departure from spherical symmetry increases, comparing with recent investigations of the real scalar field. We present a series of well-tuned numerical results and document shifts of the power-law exponent and periods as a function of the degree of asphericity of the initial data. 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.
Future Roadmap for Readers
This study explores gravitational collapse involving a massless complex scalar field minimally coupled to general relativity. The research aims to investigate the behavior of solutions near the threshold of collapse as the departure from spherical symmetry increases. The roadmap for readers is outlined below:
1. Understanding the background
Before diving into the specific research, it is important to grasp some key concepts. The article mentions critical phenomena in gravitational collapse characterized by universal power-laws and periodicities near the threshold of collapse. Readers should familiarize themselves with the basics of gravitational collapse, numerical relativity, and matter models.
2. Exploring the limitations of symmetry
The article highlights recent research suggesting a breakdown of universality of solutions in twist-free axisymmetric vacuum collapse. Readers should delve into the challenges faced when dealing with less symmetric scenarios in gravitational collapse.
3. Investigating a massless complex scalar field
The study focuses on gravitational collapse involving a massless complex scalar field. Readers should gain an understanding of this specific field and its role within general relativity.
4. Examining the numerical results
The study utilizes the pseudospectral code BAMPS to investigate a neighborhood of the spherically symmetric critical solution in phase space with aspherical departures from it. Readers should analyze the presented numerical results, which highlight shifts in power-law exponents and periods as a function of asphericity of the initial data.
5. Bifurcation of collapse and the role of gravitational waves
In highly aspherical settings, the collapse bifurcates on the symmetry axis, but away from the origin. The article suggests that gravitational waves may be driving this collapse. Readers should explore the evidence presented and evaluate the role of gravitational waves in the collapse process.
Challenges and Opportunities on the Horizon
- Challenge: The generalization of collapse to less symmetric scenarios is identified as a subtle task. Researchers will face difficulties in analyzing and understanding the behavior of solutions in these scenarios.
- Opportunity: This research provides an opportunity to deepen our understanding of gravitational collapse in scenarios with less symmetry. It opens avenues for further investigation and potential breakthroughs in numerical relativity.
- Challenge: Asphericity of initial data introduces complexities in the analysis. Researchers will need to address these challenges to accurately interpret the numerical results and draw meaningful conclusions.
- Opportunity: The exploration of aspherical departures from the spherically symmetric critical solution presents an opportunity to uncover new insights and patterns in gravitational collapse. This may expand our knowledge of the behavior of spacetime near the threshold of collapse.
- Challenge: Determining the role of gravitational waves in highly aspherical settings requires careful evaluation and analysis. Researchers will need to assess the evidence and potentially develop innovative techniques to study the influence of gravitational waves.
- Opportunity: If gravitational waves are indeed found to drive collapse in highly aspherical scenarios, it would mark a significant advancement in our understanding of the collapse process. This could have implications for astrophysics and the study of black holes.
Summary
This study investigates the behavior of solutions near the threshold of collapse in scenarios involving a massless complex scalar field and gravitational collapse. The research builds upon previous work on critical phenomena in gravitational collapse and examines the effects of asphericity and the potential role of gravitational waves. While challenges exist in generalizing collapse to less symmetric scenarios and analyzing aspherical departures, this research presents opportunities for expanding our knowledge and potentially making breakthroughs in numerical relativity and astrophysics.