BV-BFV approach to General Relativity, Einstein-Hilbert action
Alberto S. Cattaneo, Michele Schiavina
TL;DR
This paper demonstrates that general relativity can be formulated within the BV-BFV framework, linking bulk and boundary data, and recovering the canonical formulation in a unified geometric approach.
Contribution
It introduces a BV-BFV formulation for general relativity in the ADM formalism, establishing a consistent boundary-bulk data correspondence.
Findings
BV data on the bulk induces BFV data on the boundary
Canonical formulation of general relativity is recovered
Framework applies to manifolds with boundary in arbitrary dimensions
Abstract
The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered in a straightforward way.
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