A Wheeler type Gauss Law for a Gravitational Monopole.
Abstract
We showed the existence of \textit{Gauss law} for a Gravitational Monopole (satisfying Einstein's field equations) following the traditions of electro-magneto statics, and ideas of Wheeler emphasizing on \textit{charge without charge}, being only the property of the ambient space,$$ \underset{\Sigma}{\oiint} \partial_\al \zeta n^\al d \Sigma = 4 \pi n,\;\; n \in \Z .$$ It can also be seen via an argument given in the introduction that the third-fundamendal group $\pi_3$ of the Gravitational Monopole is $\Z $. It is as if the the Gravitational Monopole is already \textit{first quantized} but without being first quantized. This may resonate with Wheeler's idea and we call it \textit{quantization without quantization}.
Fields of Study & Subjects
Relativity and Gravitational Theory
Black Holes and Theoretical Physics
Quantum and Classical Electrodynamics
Publication details
- Journal / source
- HAL (Le Centre pour la Communication Scientifique Directe)
- Publication date
- 7 January 2026
- Language
- EN
- Document type
- Preprint