arXiv subjects

Hongguang Liu

Publications and source records attributed to Hongguang Liu.

At least 19 recordsLinked to original sources

arXiv2026

Holonomy Reconstruction and Character Varieties of Lorentzian Curved Tetrahedra

We give a recognition and reconstruction theorem for finite strictly convex tetrahedra in ${\rm dS}^3$ and ${\rm AdS}^3$ with spacelike, timelike, or null faces. The input consists of four nontrivial based ${\rm SO}^+(1,2)$ holonomies satisfying the closure relation. We construct their Gram data and give a global condition ensuring that the reconstructed tetrahedron lies within the required geometric domain. This condition is strict copositivity of the signed inverse Gram form on the outward branch. Together with nondegeneracy of the Gram data, it guarantees a unique finite tetrahedron up to ambient isometry, with exactly the prescribed Levi--Civita face holonomies. We express this criterion as finitely many polynomial inequalities in trace coordinates, leading to an identification of the finite tetrahedra and a subset of the relative ${\rm SL}(2,\mathbb R)$ character varieties of the four-holed sphere. We also discuss the degenerate Gram strata, vector closure in the curvature-zero limit, and the projective dual tetrahedra, which include ideal and hyperideal tetrahedral sectors. The results provide classical geometric input for quantizing Lorentzian curved tetrahedra and for quantum gravity models with a nonzero cosmological constant.

math-ph↗

arXiv2026

Probing mass inflation in polymerized vacuum regular black holes via colliding null shells

We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravity and constitute effective quantum-gravity solutions that admit a Birkhoff-type theorem, rendering them unique within the considered framework. We show that such inner-extremal horizon configurations exist only for a finely tuned value of the mass determined by the parameters of the theory. Building on this construction, together with the corresponding non-degenerate regular black hole solutions, we perform a generic analysis of the mass inflation phenomenon in four-dimensional spacetimes using a colliding null-shell setup near the inner horizon. We identify the conditions under which mass inflation becomes significant and examine how the presence of a minimal length scale affects this behavior, with particular emphasis on the case where such a scale is motivated by loop quantum gravity. Finally, we comment on the stability of these configurations under the null-shell perturbations considered in our analysis.

gr-qc↗

arXiv2026

Regular ultracompact objects with anti-de Sitter cores as polymerized vacuum solutions

We present a systematic derivation of regular black hole solutions -- and their horizonless counterparts -- that achieve regularization via an anti-de Sitter core. These geometries emerge as polymerized vacuum solutions inspired by loop quantum gravity, constituting effective quantum gravity configurations that admit a Birkhoff-type theorem and are uniquely determined by their mass. Using an auxiliary relational dust clock, together with the absence of gravitational waves in spherical symmetry, we exploit the structural ultralocality of the system to decompose the dynamics into independent shell degrees of freedom. The dust field acts as a reference clock for deparameterization and does not source the vacuum geometries considered here. These assumptions tightly constrain the Lemaitre-Tolman-Bondi shell Hamiltonian to a factorized form and the static vacuum metric function to a universal expression. We examine the possibility of a bounce and analyze how its presence is encoded, or missed, in finite-order effective truncations of the full model. The procedure for deriving the explicit physical Hamiltonian is described for a generic case before specializing to a specific model of interest. Finally, we construct a four-dimensional covariant completion of the spatially covariant Lagrangian, showing that it belongs to the class of generalized extended mimetic gravity models.

gr-qc↗

arXiv2026

Asymptotic Symmetries of the Holst Action at Spatial Infinity: Including Supertranslations

We investigate the asymptotic symmetries of General Relativity at spatial infinity within the first-order formalism described by the Holst action. Employing the covariant phase space method, we propose a set of relaxed boundary conditions for the co-tetrad and Lorentz connection that admit the full Bondi-Metzner-Sachs (BMS) group, including non-trivial supertranslations, which are typically eliminated in standard treatments. We demonstrate that the logarithmic divergences appearing in the symplectic structure can be removed by imposing specific, symmetry-preserving parity conditions on the asymptotic fields without suppressing the supertranslation sector. A detailed analysis of the conserved charges reveals that the Holst term contributes non-trivially to the charge variations due to the linear growth of Lorentz generators. We show that the naive surface integrals for the Holst charges exhibit linear divergences arising from the rotation of the background tetrad. These divergences are successfully regularized by supplementing the asymptotic symmetry generator with a compensating internal Lorentz gauge transformation defined to preserve the background structure. The resulting charges are manifestly finite and integrable. Crucially, we prove that while the Holst modification shifts the charges associated with Lorentz boosts and rotations, it leaves the supertranslation charges identically invariant. This framework provides a consistent derivation of the full BMS algebra at spatial infinity in terms of Ashtekar-Barbero variables, offering new insights into the role of the Immirzi parameter in classical and quantum gravity.

gr-qc↗

arXiv2026

Beyond Expectation Values: Generalized Semiclassical Expansions for Matrix Elements of Gauge Coherent States

We derive an asymptotic expansion for off-diagonal coherent-state matrix elements of non-polynomial operators in gauge theories admitting holomorphic coherent-state representations. The derivation combines stationary-phase analysis with an operator-level treatment of the Taylor remainder, and yields explicit semiclassical error control under stated assumptions. As a primary application, we formulate the expansion for volume and flux related operators in Loop Quantum Gravity and compare it with the standard diagonal expansion proposed in arXiv:gr-qc/0607101. By organizing the expansion around the genuine off-diagonal Berezin symbol rather than a diagonal expectation value, the resulting formula preserves the full holomorphic structure of the geometric phase and reproduces benchmark matrix elements accurately in the numerical regimes tested here, particularly when the coherent-state labels are well separated.

gr-qc↗

arXiv2026

Bridging Quantum and Semiclassical Volume: A Numerical Study of Coherent State Matrix Elements in Loop Quantum Gravity

In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a broad class of gauge-variant and gauge-invariant spin-network states. This algorithm is later used to calculate the coherent state expectation value and coherent state matrix elements of the volume operator. By comparing the results generated by our numerical model with the analytical results in various scenarios at the near-semiclassical region, not only is our numerical model validated with high accuracy, but it also provides a complete picture of how the full quantum action of the volume operator connects with its semiclassical approximations. We further find that the maximal eigenvalue approaches the classical polyhedral volume in the semiclassical regime. For irregular geometries, we also observe that the relative volume magnitudes can change in the deep quantum regime.

gr-qc↗

arXiv2026

Investigation of the gravitational dust collapse of the LQG-inspired effective asymmetric bounce model

We investigate gravitational dust collapse within an effective loop quantum gravity (LQG)-inspired model exhibiting an asymmetric bounce in the marginally bound case. This work extends previous studies, which have predominantly focused on models with either symmetric bounces or asymmetric bounces restricted to homogeneous dust configurations. Our analysis emphasises the phenomenological implications of the model through a combination of analytical and numerical investigations, with particular attention to singularity resolution and the formation of trapped surfaces. As in symmetric bounce models, the central curvature singularity inside the collapsing dust cloud is resolved. However, in contrast to the symmetric case, we find that a singularity emerges in the polymerised vacuum region during the bounce phase. This singularity can be identified as a shell-crossing singularity and exhibits the expected power-law behaviour of curvature scalars. Furthermore, likewise to the symmetric bounce models, we find a critical mass threshold governing the formation of inner and outer horizons in the pre-bounce phase. No analogous critical mass restriction arises for the formation of the inner horizon in the post-bounce phase, highlighting a qualitative difference between the pre- and post-bounce dynamics.

gr-qc↗

arXiv2025

From Principles to Effective Models: A Constructive Framework for Effective Covariant Actions with a Unique Vacuum Solution

The absence of Birkhoff's theorem in effective quantum gravity models leads to a fundamental ambiguity in the vacuum sector, where a priori no unique vacuum solution exists. As a result, phenomenological investigations of the physical implications of these models have been made more difficult. We address this challenge by establishing a constructive framework which allows to formulate 4D covariant actions from the physical nature of the systems's degrees of freedom, which are dust and gravity, together with two guiding principles. We take advantage of the non-propagating nature of a relational dust clock and the suppression of gravitational waves in spherical symmetry. This structural ultralocality allows for a decomposition of the dynamics into independent LTB shells. We further impose spatial diffeomorphism invariance and a geometric guiding principle, where the latter ensures that a unique and static vacuum solution exists. These assumptions allow to strictly constrain the LTB shell Hamiltonian to a factorised form as well as the static vacuum metric function to a universal form. This constructive framework produces a fully 4D-covariant action that belongs to the class of generalised extended mimetic gravity models. This provides the necessary consistent basis for a perturbation theory in the context of quasi-normal modes or cosmological perturbations beyond the static sector in which quantum gravity effects are also included in linear and higher order perturbations. Furthermore, for this class of models our results resolve the long-standing `curvature polymerisation ambiguity' in loop quantum cosmology by unambiguously determining how flat space modifications are extended to non-flat geometries, thus unifying the description of black holes and cosmology in a single effective framework.

gr-qc↗

arXiv2025

Quantum induced shock dynamics in gravitational collapse: insights from effective models and numerical frameworks

We explore the formation and evolution of shock waves in spherically symmetric gravitational collapse within a Loop Quantum Gravity (LQG) inspired effective framework. In this setting, the classical singularities are replaced by quantum-induced shell-crossing singularities, which are resolved through weak solutions such as shock waves. By formulating the dynamics in a generalized Painlev\'e--Gullstrand coordinate system, we derive a first-order partial differential equation that governs the propagation of the shock surface, while enforcing metric continuity via thin-shell junction conditions. To handle the non-trivial square-root structures and source terms that arise in these equations, we develop a novel numerical scheme capable of simulating quantum-corrected spacetime dynamics. Our results show that for small mass black holes near the Planck scale, the shock surface remains timelike and is shielded behind both inner and outer horizons. In the long-time limit, the shock accumulates the entire mass of the collapsing star. In contrast, for larger black hole masses, the shock surface develops spacelike segments, indicating a transition in the effective dynamics driven by quantum effects. The framework also reveals discontinuities in curvature invariants across the shock surface, which can be traced back to stress-energy redistributions caused by quantum effects. Overall, the proposed computational framework provides a general tool for modeling quantum-corrected gravitational collapse and offers new insights into black hole formations, singularity resolution, and the interplay between quantum geometry effects and effective spacetime structures.

gr-qc↗

arXiv2025

Quantum representation of reduced twisted geometry in loop quantum gravity

In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced twisted geometric variables not only describe the spatial discrete geometry more clearly, but also form a simple Poisson algebra which is analogous to that in quantum mechanics. By regularizing the reduced twisted geometric variables properly, the fundamental algebra of reduced twisted geometry is established, with the gauge invariant Hilbert space in loop quantum gravity as the corresponding quantum representation space. This quantum representation also leads to fundamental operators associated with reduced twisted geometry. Based on these fundamental operators, a new type of extrinsic curvature operator is constructed in loop quantum gravity.

gr-qc↗

arXiv2025

The one-loop effective action from the coherent state path integral of loop quantum gravity

We adopt a novel approach to combine path integral methods with Loop Quantum Gravity (LQG). Our approach builds upon the recently developed coherent state path integral formulation of LQG to compute the one-loop effective action. We compare this methodology with the conventional Quantum Field Theory (QFT) prescription for path integrals and extend the formalism to account for the dependence on boundary (coherent) states. This work aims to explore two aspects: to compare our results with the divergences observed in one-loop calculations of Einstein gravity testing UV-finiteness and to initiate an exploration of the IR effective properties of LQG. We compute the effective action around flat spacetime obtaining analytical and numerical results in the long and short wavelength approximations, respectively. Due to the one-loop dynamics of the LQG area, we find a divergence-free effective action. We study the propagator and the dynamical modes and derive the quantum equation of motion at one loop. We ensure consistency with the semiclassical approximation in the long wavelength limit and, beyond this approximation, analyze numerical scaling as the lattice size increases.

gr-qc↗

arXiv2025

Properties of 4D spinfoam quantum geometry: Results from next-to-leading order spinfoam large-$j$ asymptotics of 1-5 Pachner move

This paper proposes several criteria to probe the non-trivialities of 4-dimensional geometry that impact spinfoam amplitude. These criteria include the standard deviation of 4-volumes of the constituting 4-simplices, the smallest 4-simplex volume, and whether the directions of tetrahedron 4-normals are close to the null direction. By numerically computing and analyzing the spinfoam amplitudes up to the next-to-leading order of 1-5 Pachner move samples with the same boundary 4-simplex, we reveal the relationship between 4-dimensional geometry and spinfoam amplitudes, as large standard deviation of 4-simplex volumes and small 4-simplex volume can result in both leading order and next-to-leading order amplitudes being large. Furthermore, the numerical result indicates that the distance from tetrahedron 4-normals to the null direction has a greater impact on increasing the next-to-leading order amplitude than on the leading order amplitude, making it primarily a quantum effect.

gr-qc↗

arXiv2024

The semiclassical propagator for coherent state on twisted geometry

A new set of twisted geometric variables is introduced to parametrize the holonomy-flux phase space in loop quantum gravity. It is verified that these new geometric variables, after symplectic reduction with respect to the Gauss constraint, form a Poisson algebra which is analogue to that in quantum mechanics. This property ensures that these new geometric variables provide a simple path measure, upon which a new formulation of coherent state path integral based on twisted geometry coherent state is established in loop quantum gravity. Especially, this path integral is analytically computable by expanding the corresponding effective action around the complex evolution trajectories at second order, and the result gives the semi-classical approximation of the quantum propagator between twisted geometry coherent state in LQG.

gr-qc↗

arXiv2024

Regular black holes and their relationship to polymerized models and mimetic gravity

We present further applications of the formalism introduced by the authors in arXiv:2308.10949, which allows embedding of a broad class of generalized 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 LQG-inspired models as well as the model 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 this models to construct from a given metric in Schwarzschild-like coordinates the corresponding effective spherically symmetric model, its dynamics as an 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 look at the physical properties of the models such as the existence of weak shell-crossing singularities from a novel perspective.

gr-qc↗

arXiv2024

A Mathematica program for numerically computing real and complex critical points in 4-dimensional Lorentzian spinfoam amplitude

This work develops a comprehensive algorithm and a Mathematica program to construct boundary data and compute real and complex critical points in spinfoam amplitudes. Our approach covers both spacelike tetrahedra and triangles in the EPRL model and timelike tetrahedra and triangles in the Conrady-Hnybida extension, aiming at addressing a wide range of physical scenarios such as cosmology and black holes. Starting with a single 4-simplex, we explain how to numerically construct boundary data and corresponding real critical points from any nondegenerate 4-simplex geometry. Extending this to the simplicial complex, we demonstrate the algorithm for constructing boundary data and critical points using examples with two 4-simplices sharing an internal tetrahedron. By revisiting the $Δ_3$ triangulation with curved geometry, we demonstrate the numerical computation of the real critical point corresponding to the flat geometry and the deformation to the complex critical points. Additionally, the program evaluates the spinfoam action at the critical points and compare to the Regge action.

gr-qc↗

arXiv2024

Cosmological Dynamics from Covariant Loop Quantum Gravity with Scalar Matter

We study homogenous and isotropic quantum cosmology using the spinfoam formalism of Loop Quantum Gravity (LQG). We define a coupling of a scalar field to the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model. We employ the numerical method of complex critical points to investigate the model on two different simplicial complexes: the triangulations of a single hypercube and two connected hypercubes. We find nontrivial implications for the effective cosmological dynamics. In the single-hypercube model, the numerical results suggest an effective Friedmann equation with a scalar density that contains higher-order derivatives and a scalar potential. The scalar potential plays a role similar to a positive cosmological constant and drives an accelerated expansion of the universe. The double-hypercubes model resembles a symmetric cosmic bounce, and a similar effective Friedmann equation emerges with higher-order derivative terms in the effective scalar density, whereas the scalar potential becomes negligible.

gr-qc↗

arXiv2024

Holonomy operator for spin connection and spatial scalar curvature operator in loop quantum gravity

In this article we propose a new construction of the spatial scalar curvature operator in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a graph in terms of the twisted geometry variables, and we check that this expression reproduces the spin connection in terms of triads in a certain continuum limit. The spatial scalar curvature in terms of twisted geometry is obtained by considering the composition of the holonomy of the spin connection on the loops. With the twisted geometry parametrization of the holonomy-flux phase space, we further express the holonomy of the spin connection and the spatial scalar curvature on a graph in terms of fluxes. Finally, they are promoted as well-defined operators by replacing the fluxes with ordered flux operators.

gr-qc↗

arXiv2023

Embedding generalized LTB models in polymerized spherically symmetric spacetimes

We generalize the existing works on the way (generalized) LTB models can be embedded into polymerized spherically symmetric models in several aspects. We re-examine such an embedding at the classical level and show that a suitable LTB condition can only be treated as a gauge fixing in the non-marginally bound case, while in the marginally bound case it must be considered as an additional first class constraint. A novel aspect of our formalism, based on the effective equations of motion, is to derive compatible dynamics LTB conditions for polymerized models by using holonomy and inverse triad corrections simultaneously, whereas in earlier work these were only considered separately. Further, our formalism allows to derive compatible LTB conditions for a vast of class of polymerized models available in the current literature. Within this broader class of polymerizations there are effective models contained for which the classical LTB condition is a compatible one. Our results show that there exist a class of effective models for which the dynamics decouples completely along the radial direction. It turns out that this subsector is strongly linked to the property that in the temporally gauge fixed model, the algebra of the geometric contribution to the Hamiltonian constraint and the spatial diffeomorphism constraint is closed. We finally apply the formalism to existing models from the literature and compare our results to the existing ones.

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