arXiv:2505.13513v1 Announce Type: new
Abstract: The gauge-theoretical method introduced in our previous paper is applied to solving the axisymmetric and static Einstein-Maxwell equations. We obtain the solutions of non-Weyl class, where the gravitational and electric or magnetic potentials are not functionally related. In the electrostatic case, we show that the obtained solution coincides with the solution given by Bonnor in 1979. In the magnetostatic case, we present a solution describing the gravitational field created by two magnetically charged masses. In this solution, we show a case where the Dirac string does not stretch to spatial infinity but lies between the magnetically charged masses.
Future Roadmap
Potential Challenges:
- Integration of gauge-theoretical methods into broader physics frameworks
- Verification and validation of solutions in practical scenarios
- Applicability of solutions to real-world problems
- Understanding the implications of non-Weyl class solutions
Opportunities on the Horizon:
- Further exploration of non-functionally related potentials in gravitational and electromagnetic fields
- Development of new mathematical tools for solving complex field equations
- Integration of gauge-theoretical methods into advanced technology applications
- Potential discovery of new physical phenomena through unconventional solutions
With the advancements in gauge-theoretical methods for solving complex field equations, the future holds promise for exploring new frontiers in gravitational and electromagnetic field interactions. By addressing challenges and seizing opportunities on the horizon, researchers can pave the way for groundbreaking discoveries in theoretical and applied physics.