Affine Dynamics with Torsion
arXiv:1512.03227 · doi:10.1140/epjc/s10052-016-4015-y
Abstract
In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schrödinger, we construct and analyze different affine gravities based on the determinants of the Ricci tensor, the torsion tensor, the Riemann tensor and their combinations. In each case we reduce equations of motion to their simplest forms and give a detailed analysis of their solutions. Our analyses lead to the construction of the affine connection in terms of the curvature and torsion tensors. Our solutions of the dynamical equations show that the curvature tensors at different points are correlated via non-local, exponential rescaling factors determined by the torsion tensor.
arXiv comment25 pages, typos corrected
References in corpus (14)
- Physical Aspects of the Space-Time Torsion
- Eddington's theory of gravity and its progeny
- Affine theory of gravitation
- Universality of affine formulation in General Relativity theory
- On the nonsymmetric purely affine gravity
- Classical Physics: Spacetime and Fields
- Riemann-Eddington theory: Incorporating matter, degravitating the cosmological constant
- Conformal Transformations in Metric-Affine Gravity and Ghosts
- A unified, purely affine theory of gravitation and electromagnetism
- Eddington's Gravity in Immersed Spacetime
- Separate Einstein-Eddington Spaces and the Cosmological Constant
- A Mechanism of Ultraviolet Naturalness
- Integrable Conformal Field Theory in Four Dimensions and Fourth-Rank Geometry
- Invariant and polynomial identities for higher rank matrices