arXiv:2406.03552v1 Announce Type: new
Abstract: Recently, spherical and static flat space solitons (balls) and self-gravitating, everywhere regular, asymptotically flat solitons (stars) were constructed in an Einstein-Proca-Higgs model [1], where a complex vector field gains mass by coupling to a real scalar field with a Higgs-type potential. The Proca-Higgs model serves as a UV completion of a complex Proca model with self-interactions. Here, we construct and examine the mathematical and physical properties of rotating configurations. In particular, rotation allows horizon-bearing solutions, including stationary clouds surrounding Kerr black holes and their non-linear continuation into black holes with Proca-Higgs hair.
Future Roadmap: Challenges and Opportunities
1. Further Exploration of Rotating Configurations
The construction and examination of rotating configurations in the Einstein-Proca-Higgs model opens up new avenues for research. Continued exploration of these configurations will allow for a deeper understanding of their mathematical and physical properties.
2. Investigation of Horizon-Bearing Solutions
The presence of horizon-bearing solutions indicates the possibility of stationary clouds surrounding Kerr black holes. Investigating these solutions and studying their behavior will provide valuable insights into the dynamics of black holes and their interaction with matter fields.
3. Non-Linear Continuation into Black Holes with Proca-Higgs Hair
By studying the non-linear continuation of the rotating configurations, it becomes possible to understand the formation and properties of black holes with Proca-Higgs hair. This opens the door to exploring the effects of the Proca vector field and Higgs scalar field on the geometry and dynamics of black holes.
4. Mathematical and Physical Analysis
A comprehensive analysis of the mathematical and physical properties of the rotating configurations and their implications is crucial. This includes investigating their stability, energy-momentum content, and effect on the spacetime geometry. Such analysis will provide a solid foundation for future theoretical and observational studies.
5. Potential Challenges
- Complexity of Numerical Simulations: The construction and examination of rotating configurations in the Einstein-Proca-Higgs model may require complex numerical simulations. Overcoming computational challenges and developing efficient numerical techniques will be crucial.
- Theoretical Framework: Exploring rotating configurations and their implications may require a solid theoretical framework that can handle the intricate interplay between the Einstein field equations, Proca-Higgs model, and rotating solutions.
6. Potential Opportunities
- Advancement in Black Hole Studies: Investigating rotating configurations and their non-linear continuation into black holes with Proca-Higgs hair has the potential to advance our understanding of black holes and their interaction with matter fields.
- Implications for Fundamental Physics: Understanding the properties of rotating configurations in the Einstein-Proca-Higgs model can have broader implications for fundamental physics, such as particle physics and cosmology.
In conclusion, the study of rotating configurations in the Einstein-Proca-Higgs model presents exciting opportunities for further research. By exploring these configurations and their implications, researchers can deepen our understanding of black holes, matter fields, and fundamental physics as a whole. However, it is important to address potential challenges in numerical simulations and theoretical frameworks to fully exploit the opportunities these configurations offer.