Hamiltonian form of `Carroll' gravity

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.

Version published in Phys. Rev. D

References in corpus (8)

• Flat Holography: Aspects of the dual field theory
• Topological Interpretation of Barbero-Immirzi Parameter
• Magnetic Carrollian gravity from the Carroll algebra
• A Hamiltonian Formulation of the BKL Conjecture
• Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture
• New solutions in pure gravity with degenerate tetrads
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• The gauging procedure and carrollian gravity

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