Spherically symmetric gravitating shell as a reparametrization invariant system

Abstract

The subject of this paper are spherically symmetric thin shells made of barotropic ideal fluid and moving under the influence of their own gravitational field as well as that of a central black hole; the cosmological constant is assumed to be zero. The general super-Hamiltonian derived in a previous paper is rewritten for this spherically symmetric special case. The dependence of the resulting action on the gravitational variables is trivialized by a transformation due to Kuchař. The resulting variational principle depends only on shell variables, is reparametrization invariant, and includes both first- and second-class constraints. Several equivalent forms of the constrained system are written down. Exclusion of the second-class constraints leads to a super-Hamiltonian which appears to overlap with that by Ansoldi et al. in a quarter of the phase space. As Kuchař' variables are singular at the horizons of both Schwarzschild spacetimes inside and outside the shell, the dynamics is first well-defined only inside of 16 disjoint sectors. The 16 sectors are, however, shown to be contained in a single, connected symplectic manifold and the constraints are extended to this manifold by continuity. Poisson bracket between no two independent spacetime coordinates of the shell vanish at any intersection of two horizons.

Some sign errors are corrected and a new result is added: Poisson brackets between no two independent spacetime coordinates of the shell vanish at any intersection of two horizons

References in corpus (6)

• Hamiltonian spacetime dynamics with a spherical null-dust shell
• 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
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Cited by in corpus (21)

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• Hamiltonian Treatment of the Gravitational Collapse of Thin Shells
• Quantization of Midisuperspace Models
• Covariant gauge fixing and Kuchar decomposition
• Schrodinger formalism, black hole horizons and singularity behavior
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Gravitational Collapse of a Shell of Quantized Matter
• Experimental tests of pseudo-complex General Relativity
• Effective Action and Thermodynamics of Radiating Shells in General Relativity
• Flat foliations of spherically symmetric geometries
• WKB metastable quantum states of a de Sitter--Reissner-Nordstroem dust shell
• On the variational principle for dust shells in General Relativity
• Hamiltonian formalism for the Oppenheimer-Snyder model
• Shell-mediated tunnelling between (anti-)de Sitter vacua
• Relation between the guessed and the derived super-Hamiltonians for spherically symmetric shells
• Classical dynamics and stability of collapsing thick shells of matter
• 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
• Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell
• Black hole interacting with matter as a simple dynamical system
• Cylindrically symmetric 2+1 gravity in terms of global variables:quantum dynamics