Covariance in models of loop quantum gravity: Spherical symmetry

Abstract

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the moredifficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in spacetime appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

On the viability of regular black holes

“…The most general situation is analyzed below. In this case ∆M is of order n , where n ≥ 2 is the first natural number for which 10) so that σ = n and…”

“…In this sense, a rather conservative approach is to take seriously the hypothesis that any successful theory of quantum gravity should be able to remain predictive at the wouldbe singular regions in general relativity [8][9][10], being capable to provide at least an effective and nonsingular geometric description of the spacetime there [11,12]. Regular black hole models are in this sense a useful test-bed for exploring minimal, localized, departures from classical black hole geometries and understanding if these new aspects can lead to resolution of the classical and quantum questions mentioned above.…”

Loop quantization of the Gowdy model with local rotational symmetry

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Big Bang as a Critical Point

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