The Spacetime Geometry of Fixed-Area States in Gravitational Systems

Abstract: The concept of fixed-area states has proven useful for recent studies of quantum gravity, especially in connection with gravitational holography. We explore the Lorentz-signature spacetime geometry intrinsic to such fixed-area states in this paper. This contrasts with previous treatments which focused instead on Euclidean-signature saddles for path integrals that prepare such states. We analyze general features of fixed-area state geometries and construct explicit examples. The spacetime metrics are real at real times and have no conical singularities. With enough symmetry the classical metrics are in fact smooth, though more generally their curvatures feature power-law divergences along null congruences launched orthogonally from the fixed-area surface. While we argue that such divergences are not problematic at the classical level, quantum fields in fixed-area states feature stronger divergences. At the quantum level we thus expect fixed-area states to be well-defined only when the fixed-area surface is appropriately smeared.