Group quantization of the black hole minisuperspace

Abstract

The emergence of nontrivial symmetries for black holes minisuperspaces has been recently pointed out. These Noether symmetries possess non-null charges and hence map physical solutions to different ones. The symmetry group is isomorphic to the finite-dimensional Poincaré group ISO(2,1), whose irreducible representations are well known. This structure is used to build a consistent quantum theory of black hole minisuperspace. This has, among other consequences, the striking consequence of implying a continuous spectrum for the mass operator. Following loop quantum cosmology, we obtain a regularization scheme compatible with the symmetry structure. It is possible to study the evolution of coherent states following the classical trajectories in the low curvature regime. We show that this produces an effective metric where the singularity is replaced by a Killing horizon merging two asymptotically flat regions. The quantum correction comes from a fundamental discreteness of spacetime, and the uncertainty on the energy of the system. Remarkably, the effective evolution of semiclassical states is described by an effective Hamiltonian, related to the original one through a canonical transformation.

arXiv comment22 pages + 4 pages of appendix, 2 figures

References in corpus (60)

• Background Independent Quantum Gravity: A Status Report
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Absence of Singularity in Loop Quantum Cosmology
• The Spin Foam Approach to Quantum Gravity
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Spectroscopy of the quantum black hole
• Quantum geometry and the Schwarzschild singularity
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Quantum Transfiguration of Kruskal Black Holes
• Quantum gravity, shadow states, and quantum mechanics
• Loop quantum black hole
• Quantum Extension of the Kruskal Space-time
• Loop Quantum Dynamics of the Schwarzschild Interior
• Polymer Quantum Mechanics and its Continuum Limit
• Loop quantization of the Schwarzschild interior revisited
• Area spectrum of the Schwarzschild black hole
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Effective line elements and black-hole models in canonical (loop) quantum gravity
• On the Hamiltonian Constraint of Loop Quantum Cosmology
• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Covariance in models of loop quantum gravity: Spherical symmetry
• On the regularization ambiguities in loop quantum gravity
• Polymer Schwarzschild black hole: An effective metric
• Loop quantization of spherically symmetric midi-superspaces : the interior problem
• Black hole collapse and bounce in effective loop quantum gravity
• Quantum gravity of dust collapse: shock waves from black holes
• (b,v)-type variables for black to white hole transitions in effective loop quantum gravity
• Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition
• Properties of a recent quantum extension of the Kruskal geometry
• Loop quantum cosmology of k=1 FRW: A tale of two bounces
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• On effective loop quantum geometry of Schwarzschild interior
• Hawking radiation by spherically-symmetric static black holes for all spins: I -- Teukolsky equations and potentials
• Mass Quantization of the Schwarzschild Black Hole
• The Projective Unitary Irreducible Representations of the Poincaré Group in 1+2 Dimensions
• Emergence of product of constant curvature spaces in loop quantum cosmology
• Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
• Refined Algebraic Quantization: Systems with a single constraint
• The Evolution of $\Lambda$ Black Holes in the Mini-Superspace Approximation of Loop Quantum Gravity
• A note on the Hamiltonian as a polymerisation parameter
• Inhomogeneities, loop quantum gravity corrections, constraint algebra and general covariance
• The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Group Theoretical Quantization of a Phase Space S^1 x R^+ and the Mass Spectrum of Schwarzschild Black Holes in D Space-Time Dimensions
• Symmetries of the Black Hole Interior and Singularity Regularization
• Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Polymer Quantum Cosmology: Lifting quantization ambiguities using a $SL(2,\mathbb{R})$ conformal symmetry
• Effective Quantum Dust Collapse via Surface Matching
• Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
• Black hole mass spectrum vs spectrum of Hawking radiation
• Loop quantum cosmology of k=1 FLRW: Effects of inverse volume corrections
• Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
• The Cosmological Spinor
• Path integral renormalisation in loop quantum cosmology
• Hawking radiation by spherically-symmetric static black holes for all spins: II -- Numerical emission rates, analytical limits and new constraints

Cited by in corpus (1)

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