Gravitation as Plastic Distortion of the Lorentz Vacuum

Abstract

In this chapter we will introduce some notation in Section 5.1 and, then, in Section 5.2 we will present the Lagrangian for the free gravitational field ${\mbox{ h}}^{\clubsuit} : sec \wedge^1T^ * U \to \sec \wedge^1T^ * U$. In Section 5.3, dedicated to the derivation of the equation of motion for ${\mbox{ h}}^{\clubsuit}$ that follows from a variational principle, we will see the power of the mathematical methods developed in Chapters 2, 3 and 4. In Section 5 we will present the Lagrangian for the gravitational field plus a matter field which includes also a cosmological constant term and, then, will derive the equations of motion for the gravitational field.