Spacetime geometry from canonical spherical gravity

TL;DR

This paper develops a general covariant canonical framework for vacuum spherical gravity, deriving a broad family of Hamiltonian constraints that define diverse spacetime geometries without propagating degrees of freedom.

Contribution

It introduces a new class of Hamiltonian constraints for spherical gravity that preserve covariance and generalize Einstein's theory, allowing for rich geometric structures.

Findings

Family of Hamiltonian constraints depends on seven free functions

Geometries are covariant and gauge-independent

No propagating degrees of freedom in the models

Abstract

We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order spatial derivatives of the triad variables, and obey certain specific covariance conditions. These conditions ensure that the dynamics generated by such family univocally defines a spacetime geometry, independently of gauge or coordinates choices. This analysis generalizes the Hamiltonian constraint of general relativity, though keeping intact the covariance of the theory, and leads to a rich variety of new geometries. We find that the resulting geometries depend on seven free functions of one scalar variable, and we study their generic features. By construction, there are no propagating degrees of freedom in the theory. However, we also show that it is possible to add matter to the system by simply following the usual minimal-coupling prescription, which leads to novel models to describe dynamical scenarios.