Gravitational Entropy and Global Structure

TL;DR

Gravitational entropy is tied to obstructions to foliation in nontrivial Euclidean spacetime topology, encoded by bolts and Misner strings with a universal, background-subtracted formula for entropy. The paper develops an ADM/Hamiltonian and Euclidean-thermodynamics framework for spacetimes with a U(1) isometry and demonstrates the construction on Taub-NUT/Taub-Bolt, Israel-Wilson, Eguchi-Hanson, and S^5, showing that entropy can exceed or differ from the quarter-area horizon law. It emphasizes gravity's entropy as a global, topology-driven quantity independent of supersymmetry, with implications for information and coherence in quantum gravity. The results unify geometric obstructions with thermodynamics through boundary contributions and background subtraction.

Abstract

The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In $d$ dimensions the entropy can be expressed in terms of the $d-2$ obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of examples including spaces with nut charge. In these cases, the entropy is not just a quarter the area of the bolt, as it is for black holes.