Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime

Non-singular black holes models can be described by modified classical equations motivated by loopquantum gravity. We investigate what happens when the sine function typically used in the modi-fication is replaced by an arbitrary bounded function, a generalization meant to study the effect ofambiguities such as the choice of representation of the holonomy. A number of features can be de-termined without committing to a specific choice of functions. We find generic singularity resolution.The presence and number of horizons is determined by global features of the function regularizing theangular components of the connection, and the presence and number of bounces by global features ofthe function regularizing the time component. The trapping or anti-trapping nature of regions insidehorizons depends on the relative location with respect to eventual bounces. We use these results tocomment on some of the ambiguities of polymer black hole models.

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On the horizon area of effective loop quantum black holes

Sobrinho

Borges

Raymundo

et al. 2023

Class. Quantum Grav.

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Effective models of quantum black holes inspired by Loop Quantum Gravity (LQG) have had success in resolving the classical singularity with polymerisation procedures and by imposing the LQG area gap as a minimum area. The singularity is replaced by a hypersurface of transition from black to white holes, and a recent example is the Ashtekar, Olmedo and Singh (AOS) model for a Schwarzschild black hole. More recently, a one-parameter model, with equal masses for the black and white solutions, was suggested by Alonso-Bardaji, Brizuela and Vera (ABBV). An interesting feature of their quantisation is that the angular part of the metric retains its classical form and the horizon area is therefore the same as in the classical theory. In the present contribution we solve the dynamical equations derived from the ABBV effective Hamiltonian and, by applying the AOS minimal area condition, we obtain the scaling of the polymerisation parameter with the black hole mass. We than show that this effective model can also describe Planck scale black holes, and that the curvature and quantum corrections at the horizon are small even at this scale. By generating the exterior metric through a phase rotation in the dynamical variables, we also show that, for an asymptotic observer, the Kretschmann scalar is the same as in the classical Schwarzschild solution, but with a central mass screened by the quantum fluctuations.

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Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime

Cited by 9 publications

References 67 publications

Thermodynamic properties and entropy information of fermions in the Rindler spacetime

Thermodynamic properties and entropy information of fermions in the Rindler spacetime

Generic features of a polymer quantum black hole

On the horizon area of effective loop quantum black holes

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