Consistent gauge-fixing conditions in polymerized gravitational systems - Giesel, Kristina; Li, Bao Fei; Singh, Parampreet; Weigl, Stefan (Physical Review D, 2022)
For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge-fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical Hamiltonian. Effective descriptions encoding quantum geometric effects motivated by loop quantum gravity for symmetry-reduced models are often captured by polymerization of connection (or related) variables in gauge-fixing conditions as well as constraints. Usually, one chooses the same form of polymerization in both cases. A pertinent question is if the dynamical stability of the effective gauge-fixing conditions under the effective dynamics generated by the polymerized canonical Hamiltonian is provided by the lapse function and the shift vector obtained from the polymerization of their classical counterparts. If this is the case, then we say that gauge fixing and polymerization commute. In this manuscript we investigate these issues and obtain consistency conditions for the commutativity of gauge fixing and polymerization. Our analysis shows that such a commutativity occurs in rather special situations and reveals pitfalls in making seemingly well-motivated choices which turn out to be inconsistent with the effective dynamics. We illustrate these findings via examples of symmetry-reduced models in the loop quantization of the Schwarzschild interior and Lemaître-Tolman-Bondi spacetimes and report the noncommutativity of gauge fixing and polymerization and inherent limitations of some choices made in the literature with a consistent effective dynamics.
CRIS-Team Scopus Importer:2022-04-29

Consistent gauge-fixing conditions in polymerized gravitational systems - Giesel, Kristina; Li, Bao-Fei; Singh, Parampreet; Weigl, Stefan (Physical Review D - Particles, Fields, Gravitation and Cosmology, 2022)
For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge-fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical Hamiltonian. Effective descriptions encoding quantum geometric effects motivated by loop quantum gravity for symmetry-reduced models are often captured by polymerization of connection (or related) variables in gauge-fixing conditions as well as constraints. Usually, one chooses the same form of polymerization in both cases. A pertinent question is if the dynamical stability of the effective gauge-fixing conditions under the effective dynamics generated by the polymerized canonical Hamiltonian is provided by the lapse function and the shift vector obtained from the polymerization of their classical counterparts. If this is the case, then we say that gauge fixing and polymerization commute. In this manuscript we investigate these issues and obtain consistency conditions for the commutativity of gauge fixing and polymerization. Our analysis shows that such a commutativity occurs in rather special situations and reveals pitfalls in making seemingly well-motivated choices which turn out to be inconsistent with the effective dynamics. We illustrate these findings via examples of symmetry-reduced models in the loop quantization of the Schwarzschild interior and Lemaître-Tolman-Bondi spacetimes and report the noncommutativity of gauge fixing and polymerization and inherent limitations of some choices made in the literature with a consistent effective dynamics.<br

Effective LQC model for k=+1 isotropic cosmologies from spatial discretizations - Liegener, Klaus; Weigl, Stefan (Physical Review D, 2020)
The closed, spatially isotropic Friedmann-Lemaître-Robertson-Walker universe (k=+1) is endowed with modifications due to a discrete underlying space-structure. Motivated from loop quantum gravity techniques, a full Thiemann regularization is performed. The impact of these modifications of the single-graph-sector appearing in the scalar constraint are interpreted as physical quantum gravity effects. We investigate the form of the modified scalar constraint and its analytical approximations for k=+1 spacetimes and assume this effective constraint as the generator of dynamics on the reduced isotropic phase space. It transpires that the system still features a classical recollapse with only marginal discreteness corrections. Moreover, the initial and final singularities are resolved and we present an effective model mirroring the qualitative features of system.
CRIS-Team Scopus Importer:2020-12-11

Generalized analysis of a dust collapse in effective loop quantum gravity: Fate of shocks and covariance - Giesel, Kristina; Liu, Hongguang; Singh, Parampreet; Weigl, Stefan (Physical Review D, 2024)
Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such phenomenological studies have provided useful insights, questions remain on whether such models exhibit some of the desired properties such as consistent LTB conditions, covariance, and compatibility with the improved dynamics of loop quantum cosmology in the cosmological and LTB sector. We provide a systematic procedure to construct effective spherically symmetric models encoding LQG modifications as a 1+1 field theory models encoding these properties following the analysis in our companion paper [K. Giesel et al., Embedding generalized LTB models in polymerized spherically symmetric spacetimes, Phys. Rev. D 110, 104017 (2024)PRVDAQ2470-001010.1103/PhysRevD.110.104017]. As concrete examples of our generalized strategy, we obtain and compare with different phenomenological models, which have been investigated recently and demonstrate resolution of singularity by quantum geometry effects via a bounce. These include models with areal gauge fixing, a polymerized vacuum solution, polymerized junction conditions, and an Oppenheimer-Snyder dust collapse model. An important insight from our approach is that the dynamical equations care about the det(e) part rather than the square root of the determinant of the spatial metric. As a result, shock solutions that have been argued to exist in some models are found to be absent even if one considers coordinate transformations.
CRIS-Team Scopus Importer:2025-02-04

Implications from Different Regularisations for the Canonically Quantised k=1 FLRW Spacetime - Weigl, Stefan; Giesel, Kristina; Liegener, Klaus (2018)
In this work we present the regularisation of the Hamiltonian constraints in the context of the canonical description of general relativity (GR). We will start with the Hamiltonian formulation of GR and then introduce the Ashtekar-Barbero variables. After investigating the gauge trans- formations generated by the Hamiltonian constraints we present the holonomy-flux algebra where we also regularise the constraints. We will give a full derivation of the FLRW metric and then conclusively perform a regularisation for k=1 on spherical graphs.

Regular black holes and their relationship to polymerized models and mimetic gravity - Giesel, Kristina; Liu, Hongguang; Singh, Parampreet; Weigl, Stefan (Physical Review D, 2025)
We present further applications of the formalism introduced by K. H. Akinori Tanaka and Akio Tomiya in [Deep Learning and Phyiscs (Springer, Switzerland, 2021)], which allows the embedding of a broad class of generalized Lemaître-Tolmann-Bondi (LTB) models into effective spherically symmetric spacetimes. We focus on regular black hole models, where a broad class of models can be considered, including for example loop quantum gravity (LQG)-inspired models as well as models with a regular center, e.g., of Bardeen and Hayward. For a certain class of regular black hole models, we can formulate a Birkhoff-like theorem in LTB coordinates. We further show that, depending on the properties of the polymerization functions characterizing such regular black hole models in this formalism, the uniqueness of the effective spherically symmetric vacuum solutions might not be given in general in Schwarzschild-like coordinates. Furthermore, we introduce a reconstruction algorithm that allows for a subclass of these models to construct from a given metric in Schwarzschild-like coordinates the corresponding effective spherically symmetric model, its dynamics as a 1+1-dimensional field theory, as well as a corresponding covariant Lagrangian of extended mimetic gravity in four dimensions. Such a reconstruction allows us to obtain Lagrangians of extended mimetic gravity models for black holes with a regular center, e.g., the Bardeen and Hayward metric, as well as for effective LQG inspired models. Moreover, the reconstruction enables us to extend regular black hole models to general inhomogeneous dust collapse models. For the latter, within this formalism, we can investigate and explore various physical properties of the models such as the existence of weak shell-crossing singularities from a novel perspective.
CRIS-Team Scopus Importer:2025-04-04

Revisiting a 4-Scalar Fields Reference Model in the Context of a Loop Quantization - Weigl, Stefan; Giesel, Kristina (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2021)