Hamiltonian form of `Carroll' gravity

TL;DR

This paper formulates a Hamiltonian framework for Carroll gravity in the first-order formalism, revealing two local degrees of freedom and simplifying the Hamiltonian structure, which may facilitate future quantization efforts.

Contribution

It introduces a Hamiltonian description of Carroll gravity, including a new scaling prescription, and analyzes the degrees of freedom in this singular limit.

Findings

Two local degrees of freedom identified in Carroll gravity.

Hamiltonian constraint depends only on densitized triads and derivatives.

Simplified Hamiltonian forms are promising for quantization.

Abstract

We develop a Hamiltonian description of the `Carroll' (Levy Leblond-Sen Gupta) limit of gravity theory in the first-order formalism. Through a constraint analysis, the number of local degrees of freedom are shown to be two in this singular limit. The associated Hamiltonian constraint depends only on the densitized triad fields and their space derivatives. We also provide a scaling prescription within the Hilbert-Palatini theory to obtain the first-order analogue of the `electric' limit of canonical metric gravity. The simplicity of both these limiting Hamiltonian forms in these variables make them interesting candidates for quantization.