Mathematical structure and physical content of composite gravity in weak-field approximation

TL;DR

This paper analyzes the constraints and degrees of freedom in a composite gravity model derived from Yang-Mills theory, showing how it reproduces linearized general relativity and discusses matter coupling and background selection.

Contribution

It provides a detailed Hamiltonian analysis of the weak-field approximation of composite gravity, revealing stable solutions and coupling mechanisms that recover known gravitational physics.

Findings

Few degrees of freedom remain in the higher derivative theory.

Scalar and tensorial matter coupling mechanisms are proposed.

Linearized general relativity is reproduced in the weak-field limit.

Abstract

The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives, are analyzed in detail within a canonical Hamiltonian approach. Although this higher derivative theory involves a large number of fields, only few degrees of freedom are left, which are recognized as selected stable solutions of the underlying Yang-Mills theory. The constraint structure suggests a consistent double coupling of matter to both Yang-Mills and tetrad fields, which results in a selection among the solutions of the Yang-Mills theory in the presence of properly chosen conserved currents. Scalar and tensorial coupling mechanisms are proposed, where the latter mechanism essentially reproduces linearized general relativity. In the weak-field approximation, geodesic particle motion in static isotropic gravitational fields is found for both coupling mechanisms. An important issue is the proper Lorentz covariant criterion for choosing a background Minkowski system for the composite theory of gravity.