The Dynamical Properties Derived from the More Generalized Lagrangian Density for A Gravitational System

TL;DR

This paper extends the study of Einstein Lagrangian densities to include torsion, deriving dynamical laws and conservation principles for gravitational systems with a more generalized Lagrangian framework.

Contribution

It systematically analyzes the properties and differences of generalized Lagrangian densities with torsion compared to torsion-free cases, deriving key dynamical equations.

Findings

Derived gravitational field equations with torsion.

Established conservation laws for energy-momentum and spin densities.

Compared properties of generalized Lagrangians with and without torsion.

Abstract

The studies of the generalized Einstein Lagrangian densities without torsion are extended to those of the more generalized Lagrangian densities with torsion. The properties of the more generalized Lagrangian densities are studied systematically and thoroughly. The dynamical laws of a gravitational system such as the gravitational field equations, the conservation laws of the energy-momentum tensor densities, the conservation laws of the spin densities and the equations of motion for test particle are all derived from the Lagrangian densities. The differences between the more generalized Lagrangian densities and the generalized Einstein Lagrangian densities are discussed.