Horizons in the near-equilibrium regime

Quasi-static systems are an important concept in thermodynamics: they are dynamic but close enough to equilibrium that many properties of equilibrium systems still hold. Slowly evolving horizons are the corresponding concept for quasilocally defined black holes: they are "nearly isolated" future outer trapping horizons. This article reviews the definition and properties of these objects including both their mechanics and the role that they play in the fluid-gravity correspondence. It also introduces a new property: there is an event horizon candidate in close proximity to any slowly evolving horizon.Comment: 19 pages, 2 figures, will appear as a chapter of "Black Holes: New Horizons" edited by S. Haywar

Canonical Phase Space Formulation of Quasilocal General Relativity

We construct a Hamiltonian formulation of quasilocal general relativity using an extended phase space that includes boundary coordinates as configuration variables. This allows us to use Hamiltonian methods to derive an expression for the energy of a non-isolated region of space-time that interacts with its neighbourhood. This expression is found to be very similar to the Brown-York quasilocal energy that was originally derived by Hamilton-Jacobi methods. We examine the connection between the two formalisms and find that when the boundary conditions for the two are harmonized, the resulting quasilocal energies are identical.Comment: 31 pages, 2 figures, references added, typos corrected, section 3 revised for clarity, to appear in Classical and Quantum Gravit