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arXiv · 2505.13600

Constraints are not enough

Gary T. Horowitz·Donald Marolf·Jorge E. Santos
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Abstract

The Euclidean Einstein-Hilbert action is well-known to be unbounded below and thus to raise many questions regarding the definition of the gravitational path integral. A variety of works since the late 1980's have suggested that this problem disappears when one fixes a foliation of the spacetime and imposes the corresponding gravitational constraints. However, we show here that this approach fails with various classes of boundary conditions imposed on the foliation: compact slices without boundary, asymptotically flat, or asymptotically locally anti-de Sitter slices. We also discuss the idea of fixing the scalar curvature and Wick-rotating the conformal factor, and show that it also fails to produce an action bounded from below.

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Gary T. Horowitz, Donald Marolf, Jorge E. Santos. 2025-08-27. Constraints are not enough. https://arxiv.org/abs/2505.13600

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