Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections

Abstract

We reconsider the study of the interior of the Schwarzschild black hole now including inverse triad quantum corrections within loop quantization. We derive these corrections and show that they are are related to two parameters ${\delta }_b,{\delta }_c$ associated to the minimum length in the radial and angular directions, that enter Thiemann's trick for quantum inverse triads. Introduction of such corrections may lead to non-invariance of physical results under rescaling of the fiducial volume needed to compute the dynamics, due to noncompact topology of the model. So, we put forward two prescriptions to resolve this issue. These prescriptions amount to interchange ${\delta }_b,{\delta }_c$ in classical computations in Thiemann's trick. By implementing the inverse triad corrections we found, previous results such as singularity resolution and black-to-white hole bounce hold with different values for the minimum radius-at-bounce, and the mass of the white hole.

arXiv comment24 pages, 7 figures; v2: title, abstract and conclusion modified and some comments added for more clarity, v3: more detailed comments and computations added, matches the published version

References in corpus (14)

• Black Holes: Complementarity or Firewalls?
• Loop Quantum Cosmology: A Status Report
• Quantum geometry and the Schwarzschild singularity
• Quantum Transfiguration of Kruskal Black Holes
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Quantum gravity, shadow states, and quantum mechanics
• Loop quantum black hole
• Loop quantization of the Schwarzschild interior revisited
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Polymer Schwarzschild black hole: An effective metric
• Interior of a Schwarzschild black hole revisited
• New variables for 1+1 dimensional gravity
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model

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