It is proved that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole, and a local, geometrical prescription is proposed for the entropy, $S_{dyn}$, of a dynamical black hole.Expand

The results show that the validity of the "second law" of black hole mechanics in dynamical evolution from an initially stationary black hole to a final stationary state is equivalent to the positivity of a total Noether flux, and thus may be intimately related to the positive energy properties of the theory.Expand

In the course of the analysis, the definition of the Brown-York quasilocal energy is generalized to a much more general class of diffeomorphism invariant, Lagrangian theories of gravity.Expand

A generalization of the argument to the case in which an interior boundary is present proves that a necessary condition for a solution of the Einstein-Yang-Mills equation to be an extremum of mass at fixed area of the boundary surface is that the solution be static.Expand

It is argued that the interpretive problems of quantum gravity are not alleviated by the incorporation of observers into the theory, and a proposal for a formulation of canonical quantum gravity in which an appropriate nondynamical time parameter is present is made.Expand

It is suggested that if traversable wormholes do exist as solutions to the semiclassical equations, they cannot be macroscopic but must be ``Planck scale'', in agreement with conclusions drawn by Ford and Roman from entirely independent arguments.Expand

The main result is the demonstration that only a very restricted class of candidate infinitesimal gauge symmetries can actually arise from an exact (i.e., finite) gauge symmetry, as is necessary to realize the theory.Expand

It is argued (via consideration of other, non-Markovian models) that conservation of energy and momentum for all states is not fundamentally incompatible with causality in dynamical models in which pure states evolve to mixed states.Expand

It is proven that there do not exist any Bianchi type-IX universes which expand for an infinite time, provided only that the matter satisfies the dominant energy condition and has non-negativeâ€¦ Expand