Anomaly-free deformations of spherical general relativity coupled to matter

Abstract

A systematic approach is developed in order to obtain spherically symmetric midisuperspace models that accept holonomy modifications in the presence of matter fields with local degrees of freedom. In particular, starting from the most general Hamiltonian quadratic in radial derivatives of the variables, we obtain a family of effective modified constraints that satisfy Dirac's deformation algebra, which encodes the covariance of general relativity, and show that (scale-dependent) holonomy corrections can be consistently implemented. In vacuum, the deformed anomaly-free Hamiltonian is explicitly written in terms of three free functions and we obtain a weak observable that can be interpreted as the mass of the model. Finally, as a particular example, we present a specific covariant polymeric model that remains regular for any value of the connection components. Some of its physical implications and the relation with previous studies in the literature are commented.

Minor changes and typo corrections

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Cited by in corpus (18)

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• Constraints from Solar System tests on a covariant loop quantum black hole
• Emergent modified gravity coupled to scalar matter
• Emergent Modified Gravity
• Quasinormal modes of a nonsingular spherically symmetric black hole effective model with holonomy corrections
• MONDified Gravity
• Formation of nonsingular spherical black holes with holonomy corrections
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• Report on the session Loop Quantum Gravity: Cosmology and Black Holes of the 16th Marcel Grossmann Meeting