Nonsingular spherically symmetric black-hole model with holonomy corrections

Abstract

We present a covariant model of a spherically symmetric black hole with corrections motivated by loop quantum gravity. The effective modifications, parametrized by a positive constant $\lambda$, are implemented through a canonical transformation and a linear combination of the constraints of general relativity, in such a way that the theory remains free of anomalies and general relativity is recovered for $\lambda =0$. In addition, the corresponding metric is constructed in a fully covariant way to ensure that gauge transformations on phase space correspond to coordinate changes. The solution for each gauge choice provides a chart and corresponding line element of a spacetime solution whose geometry is unambiguously determined in terms of the parameter $\lambda$ and a constant of motion $m$. For positive values of $m$, the solution is asymptotically flat and contains a globally hyperbolic black-hole/white-hole region with a minimal spacelike hypersurface that replaces the Schwarzschild singularity. The corresponding exterior regions are isometric and, in particular, allow the computation of the ADM mass. The procedure to obtain the global causal structure of the solution yields also its maximal analytic extension.

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References in corpus (15)

• A Short Review of Loop Quantum Gravity
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes
• An effective model for the quantum Schwarzschild black hole
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Properties of a recent quantum extension of the Kruskal geometry
• Hypersurface-deformation algebroids and effective space-time models
• A no-go result for covariance in models of loop quantum gravity
• Anomaly-free deformations of spherical general relativity coupled to matter
• Non-covariance of "covariant polymerization" in models of loop quantum gravity
• Holonomy and inverse-triad corrections in spherical models coupled to matter
• A critical appraisal of the singularity theorems
• Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity
• Abelianized structures in spherically symmetric hypersurface deformations