The gravitational Hamiltonian in the presence of non-orthogonal boundaries

  title={The gravitational Hamiltonian in the presence of non-orthogonal boundaries},
  author={S. Hawking and C. J. Hunter},
  journal={Classical and Quantum Gravity},
This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces intersect the timelike boundary orthogonally. The expressions for the action and Hamiltonian are calculated and the required subtraction of a background contribution is discussed. The new features of a Hamiltonian formulation with non-orthogonal boundaries are then illustrated in two examples. 

Figures and Tables from this paper

Canonical gravity and gravitational energy 1
Hamiltonian evolution of gravitational field within a spatially com- pact world tube with non-vanishing boundary is described. It is shown that the standard A.D.M.-symplectic structure in the spaceExpand
Hamiltonians for a general dilaton gravity theory on a spacetime with a non-orthogonal, timelike or spacelike outer boundary
A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d + 1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outerExpand
Hamiltonian Structure of 2+1 Dimensional Gravity
A summary is given of some results and perspectives of the hamiltonian ADM approach to 2 + 1 dimensional gravity. After recalling the classical results for closed universes in the absence of matter,Expand
Hamiltonian, energy and entropy in general relativity with non-orthogonal boundaries
A general recipe to define, via the Noether theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge–Teitelboim-like approach applied to the variation of theExpand
ADM approach to 2+1 dimensional gravity
Abstract The canonical ADM equations are solved in terms of the conformal factor in the instantaneous York gauge. A simple derivation is given for the solution of the two body problem. A geometricalExpand
Reduced hamiltonian for intersecting shells and Hawking radiation
We consider the dynamics of one or more self gravitating shells of matter in a centrally symmetric gravitational field in the Painleve family of gauges. We give the reduced hamiltonian for twoExpand
Constrained field theories on spherically symmetric spacetimes with horizons
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory areExpand
Duality of quasilocal gravitational energy and charges with nonorthogonal boundaries
We study the duality of quasilocal energy and charges with non-orthogonal boundaries in the (2+1)-dimensional low-energy string theory. Quasilocal quantities shown in the previous work and some newExpand
Energy for N-body motion in two-dimensional gravity
A general definition of energy is given, via the Nother theorem, for the N-body problem in (1 + 1)-dimensional gravity. Within a first-order Lagrangian framework, the density of energy of a solutionExpand
ADM Approach to 2+1 Dimensional Gravity Coupled to Particles
Abstract We develop the canonical ADM approach to 2+1 dimensional gravity in the presence of point particles. The instantaneous York gauge can be applied for open universes. The sequence of canonicalExpand


Gravitational action for spacetimes with nonsmooth boundaries.
  • Hayward
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1993
The form of the action and the juncture conditions appropriate to cases in which a spacetime includes a singular matter distribution whose world history corresponds to a timelike two-dimensional surface are derived. Expand
Addendum to "Boundary Schrödinger equation in quantum geometrodynamics"
  • Hayward, Wong
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1993
The appropriate canonical form of the action functional for a spatially bounded gravitational system is determined and additional terms should have been included at the junctions of the timelike and spacelike portions of the boundary. Expand
The Gravitational Hamiltonian, action, entropy and surface terms
We give a derivation of the gravitational Hamiltonian starting from the Einstein - Hilbert action, keeping track of all surface terms. This derivation can be applied to any spacetime thatExpand
Role of surface integrals in the Hamiltonian formulation of general relativity
Abstract It is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces,Expand
Gravitational energy in spaces with compactified dimensions
We derive an energy for classical gravitational systems with compactified dimensions, and show it to be valid for geometries, such as the Kaluza-Klein monopole, whose asymptotic metrics are notExpand
Action Integrals and Partition Functions in Quantum Gravity
One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for theExpand
Boundary Schrödinger equation in quantum geometrodynamics.
  • Hayward, Wong
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1992
A geometrodynamical Schr\"odinger equation is formally derived which is expected to govern the time evolution of observables as measured on the spatial boundary of the system and it is shown that in the weak gravity limit the boundary Schr\"ODinger equation reduces to the usual functional Schr\"odoinger equation for the matter fields. Expand
Uniform Electromagnetic Field in the Theory of General Relativity
A cosmological solution of the Einstein-Maxwell's field equations, corresponding to the case of a uniform (that is, covariant constant) electromagnetic field, is derived by means of simpleExpand
On energy in 5-dimensional gravity and the mass of the Kaluza-Klein monopole
Abstract We discuss the concept of energy in higher-dimensional gravity, with special attention given to the problem of the choice of a background. Three different approaches to the calculation ofExpand
Some applications of a simple stationary line element for the Schwarzschild geometry
Guided by a Hamiltonian treatment of spherically symmetric geometry, we are led to a remarkably simple—stationary, but not static—form for the line element of Schwarzschild (and Reissner-Nordstrom)Expand