Deformed algebra and the effective dynamics of the interior of black holes

Abstract

We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the resolution of the singularity of the black hole and a minimum nonzero radius for the infalling 2-spheres, provided that the deformation parameters are chosen to be negative.

24 pages, 2 figures. arXiv admin note: text overlap with arXiv:2011.11815, v2: analysis extended, a new prescription to deal with fiducial elements introduced, figures are slightly modified and are now in color

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• Black hole interior quantization: a minimal uncertainty approach
• Modified entropies as the origin of generalized uncertainty principles
• Quantum gravitational signatures in next-generation gravitational wave detectors
• A generalized uncertainty-inspired quantum black hole
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Semiclassical resolution of the black hole singularity inspired in the minimal uncertainty approach
• Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach
• A rotating GUP black hole: metric, shadow, and bounds on quantum parameters