Gravitational entropy and global structure

S. W. Hawking; C. J. Hunter

doi:10.1103/PhysRevD.59.044025

Gravitational entropy and global structure

S. W. Hawking and C. J. Hunter

Phys. Rev. D 59, 044025 – Published 26 January 1999

An article within the collection: The Work of Stephen Hawking in Physical Review

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.

Received 26 August 1998

DOI:https://doi.org/10.1103/PhysRevD.59.044025

Collections

This article appears in the following collection:

The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."