Quantum State of a Gravitating Region

• URL: http://arxiv.org/abs/2605.28958v1
• Date: Wed, 27 May 2026 18:02:11 GMT
• Title: Quantum State of a Gravitating Region
• Abstract summary: We propose that any compact $d$-manifold with elliptic data, $mathcalJ$, prepares a quantum state $|mathcalJrangle$ on its $(d-1)$-boundary $$.<n>We obtain the von Neumann entropy by analytic continuation and find agreement with the minimal surface prescription of Bousso and Penington.
• Score: 0.10874100424278173
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose that any compact $d$-manifold with elliptic data, $\mathcal{J}$, prepares a quantum state $|\mathcal{J}\rangle$ on its $(d-1)$-boundary $σ$. Elliptic data consists of metric and field values, or their conjugates, but not both. No asymptotic structure is required. Inner products and traces are evaluated by the gravitational path integral with closed boundary conditions obtained by gluing elliptic data manifolds. In particular, we give a prescription for the Rényi entropies $S_n$ of a subregion of $σ$. In a class of examples, we find that $S_n$ is nonnegative and nonincreasing with $n$, as required for consistency. We obtain the von Neumann entropy by analytic continuation and find agreement with the minimal surface prescription of Bousso and Penington.

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