Gravitational Entropy and Global Structure

TL;DR

This paper explores the concept of gravitational entropy, linking it to topological obstructions in spacetime foliation, and provides a universal formula applicable to various Euclidean geometries including those with nut charge.

Contribution

It introduces a universal formula for gravitational entropy based on topological obstructions, extending understanding beyond black hole cases.

Findings

Entropy expressed via obstructions like bolts and Misner strings

Universal formula applicable to diverse Euclidean spacetimes

Entropy not always proportional to bolt area, especially with nut charge

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.