Gravitational Energy and the Gauge Theory Perspective

TL;DR

This paper presents a gauge theory perspective on gravity, clarifying gravitational energy through a covariant Hamiltonian formulation that yields covariant quasi-local energy and momentum expressions.

Contribution

It introduces a covariant Hamiltonian formulation of Poincare gauge gravity, providing a new way to define gravitational energy and momentum covariantly.

Findings

Covariant expressions for quasi-local energy, momentum, and angular momentum.

The importance of choosing a non-dynamic reference on the boundary.

Application to Poincare gauge theory with curvature and torsion.

Abstract

Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the Poincare group. The dynamical potentials of the Poincare gauge theory of gravity are the frame and the metric-compatible connection. The spacetime geometry has in general both curvature and torsion. Einstein's general relativity theory is a special case. Both local gauge freedom and energy are clarified via the Hamiltonian formulation. We have developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. A key feature is the necessity to choose on the boundary a non-dynamic reference. With a best matched reference one gets good quasi-local energy-momentum and angular momentum values.