Gravitational Entropy and Global Structure

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.