Gravity and BF theory defined in bounded regions
Viqar Husain, Seth Major
TL;DR
This paper investigates Einstein gravity and SU(2) BF theory within finite regions, identifying boundary conditions, surface observables, and their algebra, revealing an infinite set of observables in the bounded case.
Contribution
It provides a comprehensive analysis of boundary conditions and surface observables for gravity and BF theory in finite regions, extending previous asymptotic studies.
Findings
Infinite surface observables in bounded gravity
Surface terms contribute to the Hamiltonian
Boundary conditions are fully characterized
Abstract
We study Einstein gravity in a finite spatial region. By requiring a well-defined variational principle, we identify all local boundary conditions, derive surface observables, and compute their algebra. The observables arise as induced surface terms, which contribute to a non-vanishing Hamiltonian. Unlike the asymptotically flat case, we find that there are an infinite number of surface observables. We give a similar analysis for SU(2) BF theory.
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