Gravitational entropy and global structure

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