Spacetime Dependent Lagrangians and Electrogravity Duality

TL;DR

This paper explores the application of spacetime dependent Lagrangians to general relativity, deriving a monopole solution via electrogravity duality and establishing an upper bound on monopole mass.

Contribution

It introduces a novel approach combining spacetime dependent Lagrangians with electrogravity duality to find monopole solutions in general relativity.

Findings

Derived a Barriola-Vilenkin type monopole solution.

Established an upper bound on monopole mass.

Linked monopole properties to 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 ${\tt M}$, ${\tt M}\leq e^{(1-\alpha)/\alpha}/(1-\alpha)^{2}{\tt G}$ 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.