Physics – Classical Physics
Scientific paper
2004-02-21
Physics
Classical Physics
3 pages, Latex
Scientific paper
In this note we show the existence of the hyperbolical geometric quantum phase that is different from the ordinary trigonometric geometric quantum phase. Gravitomagnetic charge (dual mass) is the gravitational analogue of magnetic monopole in Electrodynamics; but, as will be shown here, it possesses more interesting and significant features, {\it e.g.}, it may constitute the dual matter that has different gravitational properties compared with mass. In order to describe the space-time curvature due to the topological dual mass, we construct the dual Einstein's tensor. Further investigation shows that gravitomagnetic potentials caused by dual mass are respectively analogous to the trigonometric and hyperbolic geometric phase. The study of the geometric phase and dual mass provides a valuable insight into the time evolution of quantum systems and the topological properties in General Relativity.
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