Effective loop quantization of black holes : a comparative analysis of quantization schemes.

Loop quantization of spherically symmetric black hole (BH) spacetimes has quantization ambiguities stemming from the choices (schemes) of the two polymerization parameters that characterize quantum corrections in effective loop quantum gravity (LQG). In this dissertation we systematically carry out the following investigations in the framework of the Kantowski-Sachs (KS) gauge: (a) We first study a top-down quantization that is derived from full LQG. The semi-classical approximation of this model resolves the central BH singularity and replaces it with a transition surface. The spacetime to the future of the transition surface depends on the ratio of two spin numbers involved in the model. We also find the inverse volume corrections become important only when the radius of the two-sphere is of the Planck size and are hence negligible for macroscopic BHs. (b) We study a quantization scheme recently proposed, where the polymerization parameters are the Dirac observables of the four-dimensional phase space of Ashtekar’s variables. The model predicts a white hole horizon beyond the transition surface which replaces the singularity. However, the spacetime to the future of the transition surface is unlike any of the loop quantum black holes (LQBHs) studied so far. In particular, the location of the maximal curvatures is different from the location of the transition surface that has the minimal area. (c) We systematically study all the solutions of LQBHs with constant polymerization parameters and find the classical singularity is always resolved. Additionally, assuming the black and white hole masses are equal, we identify a whole family of solutions that share all the desired properties of the Ashtekar, Olmedo and Singh model. (d) Finally, we extend the studies carried out in (c) to the Schwarzschild BH coupled with a cosmological constant (Λ) and show that for Λ > 0 there can be an appearance of large quantum effects at low curvatures. These effects can manifest as an additional black hole horizon. Although central singularity is always resolved, these limitations demonstrate the incompatibility of the KS gauge and schemes with constant polymerization parameters when a positive cosmological constant is present.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2025

Author dc:creator

• Ongole, Geeth Chandra, 1994-

Advisor dc:contributor.advisor

• Wang, Anzhong.

• Loop quantum gravity (LQG)
• Quantum black holes.
• Black holes.
• Schwarzschild metric.
• Polymerization.
• Ashtekar, Olmedo and Singh (AOS) model.
• Dirac observables.
• Cosmological constant.
• Schwarzschild de-Sitter metric.
• Kantowski-Sachs gauge.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/13831

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/13831