Spacetime Dependent Lagrangians and Electrogravity Duality

Abstract

We apply the spacetime dependent lagrangian formalism [1] to the action in general relativity. We obtain a Barriola-Vilenkin type monopole solution by exploiting theelectrogravity duality of the vacuum Einstein equations and using a modified definition of empty space. An {\it upper bound} is obtained on the monopole mass $\mathtt{M}$, $\mathtt{M}\le e^{(1-\alpha )/\alpha }/(1-\alpha {)}^2\mathtt{G}$ where $\alpha =2k$ is the global monopole charge. Keywords: global monopole, electrogravity duality, holographic principle. PACS: 11.15.-q, 11.27.+d, 14.80.Hv, 04.

4 pages, latex