Einstein Equations from Riemann-only Gravitational Actions

Details Einstein Equations from Riemann-only Gravitational Actions Einstein Equations from Riemann-only Gravitational Actions

2011-05-24

arxiv.org/abs/1105.4750v3

Physics

High Energy Physics

High Energy Physics - Theory

Added references; Modified the text; 13 pp

Scientific paper

In pure affine formalism for gravitation, we construct invariant actions constructed solely from the Riemann tensor. We do this by generalizing the notion of determinant to higher rank tensor fields. In regard to reducing to Einstein-Hilbert action in arbitrary dimensions, we show that Riemann-only actions are more natural than those based on the Ricci tensor. In spacetimes with torsion, we construct a dynamical equation for Riemann tensor itself, and show that it embodies the usual gravitational field equations.

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