LTB spacetimes in terms of Dirac observables

Abstract

The construction of Dirac observables, that is gauge invariant objects, in General Relativity is technically more complicated than in other gauge theories such as the standard model due to its more complicated gauge group which is closely related to the group of spacetime diffeomorphisms. However, the explicit and usually cumbersome expression of Dirac observables in terms of gauge non invariant quantities is irrelevant if their Poisson algebra is sufficiently simple. Precisely that can be achieved by employing the relational formalism and a specific type of matter proposed originally by Brown and Kucha{\v r}, namely pressureless dust fields. Moreover one is able to derive a compact expression for a physical Hamiltonian that drives their physical time evolution. The resulting gauge invariant Hamiltonian system is obtained by Higgs -- ing the dust scalar fields and has an infinite number of conserved charges which force the Goldstone bosons to decouple from the evolution. In previous publications we have shown that explicitly for cosmological perturbations. In this article we analyse the spherically symmetric sector of the theory and it turns out that the solutions are in one--to--one correspondence with the class of Lemaitre--Tolman--Bondi metrics. Therefore the theory is capable of properly describing the whole class of gravitational experiments that rely on the assumption of spherical symmetry.

29 pages, no figures

References in corpus (4)

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• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
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• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Spherical symmetric gravitational collapse of a dust cloud: polymerized dynamics in reduced phase space
• Towards a reduced phase space quantization in loop quantum cosmology with an inflationary potential
• Non-singular quantum gravitational dynamics of an LTB dust shell model: the role of quantization prescriptions
• Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
• Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
• Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Loop Quantum Vector-Tensor Gravity and Its Spherically Symmetric Model