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Geometric Calculus is developed for curved-space treatments of General Relativity and comparison is made with the flat-space gauge theory approach by Lasenby, Doran and Gull. Einstein’s Principle of Equivalence is… Click to show full abstract
Geometric Calculus is developed for curved-space treatments of General Relativity and comparison is made with the flat-space gauge theory approach by Lasenby, Doran and Gull. Einstein’s Principle of Equivalence is generalized to a gauge principle that provides the foundation for a new formulation of General Relativity as a Gauge Theory of Gravity on a curved spacetime manifold. Geometric Calculus provides mathematical tools that streamline the formulation and simplify calculations. The formalism automatically includes spinors so the Dirac equation is incorporated in a geometrically natural way.
Journal Title: Advances in Applied Clifford Algebras
Year Published: 2020
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