Gauge theory gravity with geometric calculus
This is the third in a series of articles promoting ``geometric algebra'' elaborated by the same author. After summarizing essential mathematical tools introduced in a preceding paper and extending them to ``geometric calculus'' applicable to differentiable manifolds, the ``gauge theory gravity'' by Lasenby, Doran, and Gull is considered. It is shown that the gauge principles of this theory generate an induced geometry on space-time that is equivalent to Riemannian geometry. In discussing the field equations and the equations of motion in gauge theory gravity and solutions to the field equations, the paper demonstrates that geometric calculus is conceptually and computationally suitable for this gauge theory approach. In particular, it is proved that, due to the displacement gauge principle of this theory, a displacement-gauge-invariant energy-momentum conservation law exists.
scientific article; zbMATH DE number 5007727
scientific article