From freely falling frames to the Lorentz gauge-symmetry group and a Hamiltonian composite theory of gravitation

TL;DR

This paper develops a Hamiltonian composite theory of gravity based on local Lorentz gauge symmetry, analyzing black-hole solutions and gravitational waves, and outlining steps toward quantization.

Contribution

It introduces a gauge-theoretic, composite approach to gravity with a Hamiltonian formulation and explicit constraints, advancing toward quantum gravity.

Findings

Exact black-hole solutions under specific coordinate conditions

Composite gravity has only four physical degrees of freedom despite large symmetry

Outlined a pathway for quantizing the nonlinear theory

Abstract

The concept of freely falling frames suggests that gravity exhibits a local Lorentz gauge symmetry and requires a background Minkowski reference frame. The gauge vector fields of a Yang-Mills-type theory can be constructed from the transformations to these local freely falling frames, thereby leading to a composite theory of gravity. We propose coordinate conditions under which an exact black-hole solution can be obtained. Our analysis of planar gravitational waves reveals that, despite the large symmetry group, composite gravity possesses only four physical degrees of freedom. We elaborate a Hamiltonian formulation of composite gravity, derive the full set of constraints for the nonlinear theory, and outline the pathway toward its quantization.