Spacetime Dependent Lagrangians and Electrogravity Duality

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 $\mathtt{M}$, ${\tt M}\leq e^{(1-\alpha)/\alpha}/(1-\alpha)^{2}{\tt G}$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.