arXiv subjects

Haida Li

Publications and source records attributed to Haida Li.

13 recordsLinked to original sources

arXiv2026

Extended spherically symmetric solutions in revised Deser--Woodard nonlocal gravity

In this work, we extend the static spherically symmetric black hole solutions of revised Deser--Woodard (D-W) nonlocal gravity. Due to the linearity of the field equations, we show that the first-order expansion around the Schwarzschild solution is linear in both the temporal metric component and the reciprocal of the radial metric component. Therefore, a mode-by-mode superposition can be properly defined for different types of correction terms. We then further study two additional asymptotically flat extensions, a logarithmically dressed correction and an exponentially suppressed correction. The logarithmically dressed correction gives a slowly decaying deviation from Schwarzschild as the radius becomes large, making it a more extended nonlocal effect, whereas the exponentially suppressed correction is localized near the horizon and shifts the horizon inward for positive correction amplitude. These correction terms are physically motivated by common mechanisms in modified gravity: Logarithmic terms are possibly related to effects of quantum corrections, and exponential terms can arise from finite-range or screened gravitational effects.

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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.

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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.

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arXiv2026

Gravitational Lensing Effect from The Revised Deser-Woodard Nonlocal Gravity

We investigate the gravitational lensing effects of a static spherically symmetric black hole (BH) within the framework of the revised Deser-Woodard (D-W) nonlocal gravity. By analyzing the deflection angle in both the weak and strong field limits, we derive several distinguishing features of the model. In the weak field limit, we report a leading-order correction to the deflection angle directly attributed to the non-local nature of the theory. In the strong field limit, we find that the lensing corrections are almost linearly dependent on the coupling parameter $\zeta$ while being exponentially suppressed by the exponent parameter $n$. Furthermore, the gravitational lensing effect in the revised D-W model at a given time shares similar scale-invariant behavior to General Relativity and conformal gravity, offering a potential pathway to distinguish it from other alternatives using astronomical observations.

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arXiv2025

Deflection of Massive Spin-$\frac{1}{2}$ Particles around Kerr Black Hole

The exact measurement of neutrino mass remains a longstanding issue. So far, there has been much success in providing an upper bound for the neutrino rest mass, both theoretically and experimentally. In this work, by exploring the critical radius of a beam of polarized quantum spin-$\frac{1}{2}$ particle deflecting around a classical Kerr black hole, we attempt to provide an additional testing ground for neutrino mass, as well as the mass of other proposed ultra-light particles yet to be determined. Notably, the quantum Dirac equation is used to derive a MPD-like equation satisfied by the polarized beam of massive spin-$\frac{1}{2}$ particles and identify the effective spin in the spin tensor with the particle's intrinsic quantum spin, confirming the previous theoretical result that the MPD equation can be in fact applied to particles' intrinsic spin. The result of this work shows that corrections of relative magnitude $>10^{-12}$ can be achieved for spin-$\frac{1}{2}$ particles with rest mass equal to $1 eV/c^2$ deflecting around a solar mass Kerr black hole. Although highly theoretical, a new method of extracting the lower bound for the neutrino mass individually is also proposed due to the behavior of the quantum spin correction.

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arXiv2025

Deparametrization and quantization of scalar-tensor gravity and its cosmological model

The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop quantum gravity. This results in a discrete time evolution of the physical states with respect to the gravitational degree of freedom in the quantum theory. In the corresponding Brans-Dicke cosmological model, the physical solutions to the quantum Hamiltonian constraint are obtained in the light of the deparametrization. The quantum dynamics indicates that the classical big bang singularity is replaced by a quantum bounce.

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arXiv2025

Particle Deflections around Microscopic Loop Quantum Black Holes with Rigorous Quantum Parameters

The detection of quantum gravity effects is highly limited in both macroscopic and microscopic scenarios: The small quantum parameter makes most large-scale observations practically indistinguishable from general relativity. While at the Planck scale, where the effect of quantum gravity is undoubtedly significant, the energy requirement is remarkably high for any test particle as a probe. In this work, by focusing on the inner-most stable circular orbit (ISCO) of both massless and massive particles around a microscopic loop quantum black hole, we show that given the current knowledge of ultra-high-energy particles, quantum corrections of relative scale $>10^{-10}$ can appear when the radius of the black hole horizon remains larger than the wavelength of high-energy Gamma rays, where the classical photon trajectory may still hold to a certain degree. In addition, more significant corrections can be observed when considering low velocity massive particles. Potentially, our results could suggest a new area for testing the effects of quantum gravity.

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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.

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arXiv2022

Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.

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arXiv2021

Entropy of black holes with arbitrary shapes in loop quantum gravity

The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is successfully applied in the scheme to calculate the entropy by the $SO(1,1)$ BF boundary theory matching loop quantum gravity in the bulk. The generating function for calculating the microscopical degrees of freedom of a given isolated horizon is obtained. Numerical computations of small black holes indicate a new entropy formula containing the quantum correction related to the partition of the horizon. Further evidence shows that, for a given horizon area, the entropy decreases as a black hole deviates from the spherically symmetric one, and the entropy formula is also well suitable for big black holes.

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arXiv2021

Manifestly Gauge-Invariant Cosmological Perturbation Theory from Full Loop Quantum Gravity

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit.

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arXiv2019

Bouncing evolution in a model of loop quantum gravity

To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The Hamiltonian operator $\hat{H}_v$ is chosen to be graph-preserving, and the matrix elements of $\hat{H}_v$ are explicitly worked out in a suitable basis. The non-trivial Euclidean part $\hat{H}_v^E$ of $\hat{H}_v$ is studied in details. It turns out that by choosing a specific symmetrization of $\hat{H}_v^E$, the dynamics driven by the Hamiltonian gives a picture of bouncing evolution. Our result in the model of full loop quantum gravity gives a significant echo of the well-known quantum bounce in the symmetry-reduced model of loop quantum cosmology, which indicates a closed relation between singularity resolution and quantum geometry.

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arXiv2017

Distinguishing f(R) theories from general relativity by gravitational lensing effect

The post-Newtonian formulation of a general class of f(R) theories is set up to 3rd order approximation. It turns out that the information of a specific form of f(R) gravity is encoded in the Yukawa potential, which is contained in the perturbative expansion of the metric components. Although the Yukawa potential is canceled in the 2nd order expression of the effective refraction index of light, detailed analysis shows that the difference of the lensing effect between the f(R) gravity and general relativity does appear at the 3rd order when $\sqrt{f''(0)/f'(0)}$ is larger than the distance $d_0$ to the gravitational source. However, the difference between these two kinds of theories will disappear in the axially symmetric spacetime region. Therefore only in very rare case the f(R) theories are distinguishable from general relativity by gravitational lensing effect at the 3rd order post-Newtonian approximation.

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