arXiv:2407.18973v1 Announce Type: new
Abstract: We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs system in the framework of Bondi coordinates. As a first step, the problem is reduced to a single first-order integro-differential equation by defining a generalized ansatz function. Then, we employ contraction mapping to show that there exists the unique fixed point of the problem. For a given small initial data, we prove the existence of a global classical solution. Finally, by introducing local mass and local charge functions in higher dimensions, we also show the completeness property of the spacetimes.
Conclusions:
- The authors have studied the Cauchy problem of the higher dimensional Einstein-Maxwell-Higgs system.
- They have utilized Bondi coordinates and reduced the problem to a single first-order integro-differential equation using a generalized ansatz function.
- They have applied contraction mapping to prove the existence of a unique fixed point of the problem.
- They have demonstrated the existence of a global classical solution for small initial data.
- They have introduced local mass and local charge functions in higher dimensions and shown the completeness property of the spacetimes.
Future Roadmap:
- To further explore the implications of the higher dimensional Einstein-Maxwell-Higgs system, future research can focus on studying the behavior of the system under different initial conditions.
- Challenges may arise in determining the existence of global solutions for larger initial data sets and investigating the stability of the solutions over time.
- Opportunities exist to analyze the physical implications of the local mass and local charge functions in higher dimensions and their relevance to other aspects of theoretical physics.
- Possibilities for extending the study to other related systems, such as the inclusion of additional fields or considering different types of coordinates, could provide valuable insights.
- Further investigation could involve the examination of the system in the presence of external perturbations or examining the behavior of the system in different spacetime geometries.