Gravity from Poincare Gauge Theory of the Fundamental Particles. I: General Formulation

Abstract

We study Poincaré gauge theory with linear and quadratic Lagrangians, where there are the translation and Lorentz gauge fields whose sources are the energy-momentum tensor and the spin tensor, respectively. Ten parameters, a, α, β, γ, a1 , …, a6, are contained in the gravity action. Most general field equations covariant under the Poincaré gauge group are derived, and also their alternative forms are obtained. For geometrical analysis the present space-time is that of Riemann-Cartan, endowed with curvature and torsion. General Relativity is recovered when a spin source vanishes and the parameters satisfy the conditions, 3a2 + 2a5 =0=a5+12a6.