Hamiltonian spacetime dynamics with a spherical null-dust shell

Abstract

We consider the Hamiltonian dynamics of spherically symmetric Einstein gravity with a thin null-dust shell, under boundary conditions that fix the evolution of the spatial hypersurfaces at the two asymptotically flat infinities of a Kruskal-like manifold. The constraints are eliminated via a Kuchar-type canonical transformation and Hamiltonian reduction. The reduced phase space $\tilde{\Gamma }$ consists of two disconnected copies of $R^4$, each associated with one direction of the shell motion. The right-moving and left-moving test shell limits can be attached to the respective components of $\tilde{\Gamma }$ as smooth boundaries with topology $R^3$. Choosing the right-hand-side and left-hand-side masses as configuration variables provides a global canonical chart on each component of $\tilde{\Gamma }$, and renders the Hamiltonian simple, but encodes the shell dynamics in the momenta in a convoluted way. Choosing the shell curvature radius and the "interior" mass as configuration variables renders the shell dynamics transparent in an arbitrarily specifiable stationary gauge "exterior" to the shell, but the resulting local canonical charts do not cover the three-dimensional subset of $\tilde{\Gamma }$ that corresponds to a horizon-straddling shell. When the evolution at the infinities is freed by introducing parametrization clocks, we find on the unreduced phase space a global canonical chart that completely decouples the physical degrees of freedom from the pure gauge degrees of freedom. Replacing one infinity by a flat interior leads to analogous results, but with the reduced phase space $R^2\cup R^2$. The utility of the results for quantization is discussed.

40 pages, REVTeX v3.1 with amsfonts and epsf, two eps figures. (Minor typos corrected; references updated.)

References in corpus (9)

• Classical and Quantum Shell Dynamics, and Vacuum Decay
• Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Instructive Properties of Quantized Gravitating Dust Shell
• Gauge Invariant Hamiltonian Formalism for Spherically Symmetric Gravitating Shells
• Spherically symmetric gravitating shell as a reparametrization invariant system
• The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant
• Reduced Phase Space Quantization of spherically symmetric Einstein-Maxwell-Theory including a cosmological constant
• Quantum Decay of Domain Walls in Cosmology II: Hamiltonian Approach

Cited by in corpus (40)

• Area spectra of the rotating BTZ black hole from quasinormal modes
• Quantum superposition principle and gravitational collapse: Scattering times for spherical shells
• Selected solutions of Einstein's field equations: their role in general relativity and astrophysics
• Embedding variables in the canonical theory of gravitating shells
• Unitary dynamics of spherical null gravitating shells
• Quantization of Midisuperspace Models
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Quantum self-gravitating collapsing matter in a quantum geometry
• Quantum Black Holes from Quantum Collapse
• Spherically symmetric gravitating shell as a reparametrization invariant system
• Brief review on black hole loop quantization
• Black hole mass spectrum vs spectrum of Hawking radiation
• WKB metastable quantum states of a de Sitter--Reissner-Nordstroem dust shell
• Emergent modified gravity: The perfect fluid and gravitational collapse
• Quantum Collapse of a Small Dust Shell
• Exact Quantum State of Collapse and Black Hole Radiation
• Toward a Quantization of Null Dust Collapse
• Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts
• Reduced Hamiltonian for intersecting shells
• Shell-mediated tunnelling between (anti-)de Sitter vacua
• Pair of null gravitating shells II. Canonical theory and embedding variables
• Quantum fluctuating geometries and the information paradox
• Pair of null gravitating shells III. Algebra of Dirac's observables
• A Partially Gauged Fixed Hamiltonian for Scalar Field Collapse
• Geometrodynamics in a spherically symmetric, static crossflow of null dust
• Geometry of crossing null shells
• Quantum Collapse of a Thin Shell Revisited
• Quasiclassical mass spectrum of the black hole model with selfgravitating dust shell
• 2+1-dimensional gravity coupled to a dust shell: quantization in terms of global phase space variables
• An action principle for the quantization of parametric theories and nonlinear quantum cosmology
• On the semiclassical treatment of Hawking radiation
• Collapsing Shells and Black Holes: a quantum analysis
• Quantum fluctuating geometries and the information paradox II
• Schrödinger-like quantum dynamics in loop quantized black holes
• Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell
• Dynamics of a self gravitating light-like matter shell with spherical symmetry
• Quantum fluctuating CGHS geometries and the information paradox
• Reduced Hamiltonian for intersecting shells and Hawking radiation
• Proper time Quantization of a Thin Shell
• Cylindrically symmetric 2+1 gravity in terms of global variables:quantum dynamics