On the tetrad theory of gravity

Mathematics – Logic

Scientific paper

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Cosmology, Gauge Theory, Gravitation Theory, Relativity, Space-Time Functions, Tetrad Theory, Cartan Space, Isotropic Media, Particle Spin, Quadratic Equations, Riemann Manifold, Schwarzschild Metric, Torsion

Scientific paper

Problems are reviewed which appear in the theory of teleparallelism (tetrad theory) based on a Lagrangian quadratic in the torsion. The possibility of adding higher-order terms is discussed. For a 'test Lagrangian', O(3)-symmetric vacuum solutions and spatially homogeneous and isotropic solutions are found. The latter contain nonsingular cosmological models. The test theory is shown to admit the Schwarzschild metric (accompanied with some torsion functions) as an exact vacuum solution. Examining Moeller's theory, it is shown that the field equations are not able to determine the teleparallel geometry sufficiently; some arguments indicate that the same applies to the test theory.

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