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Recently, two new spherically symmetric black hole models with covariance have been proposed in effective quantum gravity. Based on these models, we use the modified Newman-Janis algorithm to generate two rotating quantum-corrected black hole solutions, characterized by three parameters, the mass $M$, the spin $a$, and the quantum parameter $\zeta$. To understand the effects of the quantum parameter $\zeta$ on these two rotating black holes, we investigate in detail the horizons and static limit surfaces. By constraining the possible range of the parameters, we study the shadows cast by these rotating black holes. The results indicate that for both rotating BHs, the parameter $\zeta$ mainly affects the shadow size in the non-extremal case, while it deforms the shadow shape by arising a cuspy edge in the near-extremal case., Comment: 12 pages, 9 figures

Today's image generation systems are capable of producing realistic and high-quality images. However, user prompts often contain ambiguities, making it difficult for these systems to interpret users' potential intentions. Consequently, machines need to interact with users multiple rounds to better understand users' intents. The unpredictable costs of using or learning image generation models through multiple feedback interactions hinder their widespread adoption and full performance potential, especially for non-expert users. In this research, we aim to enhance the user-friendliness of our image generation system. To achieve this, we propose a reflective human-machine co-adaptation strategy, named RHM-CAS. Externally, the Agent engages in meaningful language interactions with users to reflect on and refine the generated images. Internally, the Agent tries to optimize the policy based on user preferences, ensuring that the final outcomes closely align with user preferences. Various experiments on different tasks demonstrate the effectiveness of the proposed method.

This work addresses the longstanding issue of general covariance in effective models of quantum gravity, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In spherically symmetric models, the concept of general covariance is formulated into precise equations. Applying the minimal requirements proposed to ensure general covariance, we derive the equations for the effective Hamiltonian constraint with the aid of imposing demands on Dirac observables. The equations yield two candidates for effective Hamiltonian constraints dependent on a quantum parameter. The resulting quantum modified black hole spacetimes are analyzed, and they overcome the limitations seen in similar spacetimes from previous works., Comment: 5+3 pages. Major revisions include the addition of an appendix and a discussion on dust coupling in the final section

Automated code generation is a pivotal capability of large language models (LLMs). However, assessing this capability in real-world scenarios remains challenging. Previous methods focus more on low-level code generation, such as model loading, instead of generating high-level codes catering for real-world tasks, such as image-to-text, text classification, in various domains. Therefore, we construct AICoderEval, a dataset focused on real-world tasks in various domains based on HuggingFace, PyTorch, and TensorFlow, along with comprehensive metrics for evaluation and enhancing LLMs' task-specific code generation capability. AICoderEval contains test cases and complete programs for automated evaluation of these tasks, covering domains such as natural language processing, computer vision, and multimodal learning. To facilitate research in this area, we open-source the AICoderEval dataset at \url{https://huggingface.co/datasets/vixuowis/AICoderEval}. After that, we propose CoderGen, an agent-based framework, to help LLMs generate codes related to real-world tasks on the constructed AICoderEval. Moreover, we train a more powerful task-specific code generation model, named AICoder, which is refined on llama-3 based on AICoderEval. Our experiments demonstrate the effectiveness of CoderGen in improving LLMs' task-specific code generation capability (by 12.00\% on pass@1 for original model and 9.50\% on pass@1 for ReAct Agent). AICoder also outperforms current code generation LLMs, indicating the great quality of the AICoderEval benchmark.

In this paper, we carry out the entanglement calculations on the coherent intertwiners. We first consider the entanglement introduced by the group-averaging of the tensor-product type intertwiner on a four-valents vertex. The result shows that the entanglement is determined by the probability distribution of recoupling spin, and this probability distribution is a well-behaved peak for the highest (and lowest) weight states. Further, we calculated explicitly the entanglement on gauge-invariant coherent intertwiner with four legs. Our numerical results show that the shape of the semiclassical polyhedron described by the coherent intertwiner can be related to the entanglement; In other words, the entanglement is controlled by the face-angle of the semiclassical polyhedron. Finally, we extend our analytical calculation to the coherent intertwiners with arbitrary number of legs., Comment: 25 pages, 12 figures

Graphical techniques provide a very useful practical device for calculations involving the so-called spin network states, which encode the quantum degrees of freedom of spatial geometry in loop quantum gravity. Graphical calculus of SU(2), which has been originally introduced in the literature in order to deal with calculations arising from the coupling of angular momenta in quantum mechanics, can be used as a simple but powerful method for computing the action of various physically interesting operators in the spin network representation. Compared with conventional manipulation of algebraic expressions, calculations in the graphical approach are typically more convenient, concise and visually transparent. The goal of this chapter is to provide an accessible introduction to graphical methods in SU(2) recoupling theory and a brief description of their use as a tool for practical calculations in loop quantum gravity. We introduce the basics of the graphical formalism, and establish the representation of the elementary states and operators of loop quantum gravity in graphical form. Several example calculations are given to illustrate the use of the graphical techniques, including a computation of the matrix elements of a Hamiltonian constraint operator in the spin network basis., Comment: 28 pages. Invited chapter for the Handbook of Quantum Gravity (editors C. Bambi, L. Modesto and I. L. Shapiro, Springer, 2023)

The quantum extension of the Kruskal spacetime indicates the existence of a companion black hole in the universe earlier than ours. It is shown that the radiations from the companion black hole can enter its horizon, pass through the deep Planck region, and show up from the white hole in our universe. These radiations inlay extra bright rings in the image of the black hole in our universe, and some of these rings appear distinctly in the shadow region. Therefore, the image of the black hole observed by us encodes the information of quantum gravity. The positions and widths of the bright rings are predicted precisely. The predictive values for supermassive black holes are universal for a quite general class of quantum-modified spacetimes with the phenomenon of black hole to white hole transition. Thus, our result opens a new experimental window to test this phenomenon predicted by quantum gravity., Comment: 6+6 pages, 6 figures, Fig. 6 and some relevant discussions is added

An alternative quantization of the gravitational Hamiltonian constraint of the $k=-1$ Friedmann-Robertson-Walker model is proposed by treating the Euclidean term and the Lorentzian term independently, mimicking the treatment of full loop quantum gravity. The resulting Hamiltonian constraint operator for the $k=-1$ model with a massless scalar field is successfully constructed, and is shown to have the corrected classical limit. Compared to the former quantization schemes in the literature where only the Euclidean term is quantized, the new quantum dynamics of the $k=-1$ model with a massless scalar field indicates that the classical big-bang singularity is replaced by an asymmetric quantum bounce., Comment: 10 pages, 3 figures; V2, 15 pages, 3 figures, version published in PRD

Recently the quantum Oppenheimer-Snyder gravitational collapse model has been proposed in loop quantum gravity, providing quantum-corrected Schwarzschild spacetimes as the exterior of the collapsing dust ball. In this paper, the quantum gravity effects on the black hole shadows in this model are studied, and the stability of the quantum-corrected black holes is also analyzed by calculating the quasinormal modes. It turns out that the quantum correction always shrinks the radius of shadows, and the quantum-corrected black holes are stable against the scalar and vector perturbations., Comment: 15 pages, 9 figures

By considering the quantum Oppenheimer-Snyder model in loop quantum cosmology, a new quantum black hole model whose metric tensor is a suitably deformed Schwarzschild one is derived. The quantum effects imply a lower bound on the mass of the black hole produced by the collapsing dust ball. For the case of larger masses where the event horizon does form, the maximal extension of the spacetime and its properties are investigated. By discussing the opposite scenario to the quantum Oppenheimer-Snyder, a quantum Swiss Cheese model is obtained with a bubble surrounded by the quantum universe. This model is analogous to black hole cosmology or fecund universes where the big bang is related to a white hole. Thus our models open a new window to cosmological phenomenology., Comment: 5+3 pages, 2 figures, revised to adapt the published version

The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a graphical derivation of the partition function of the generalized Euclidean Engle-Pereira-Rovelli-Livine (EPRL) spin-foam model is presented. On the other hand, the action of a Euclidean Hamiltonian constraint operator on certain spin network states is calculated by graphical method. It turns out that the EPRL model can provide a rigging map such that the Hamiltonian constraint operator is weakly satisfied on certain physical states for the Immirzi parameter $\beta=1$. In this sense, the quantum dynamics between the covariant and canonical formulations are consistent to each other., Comment: 19 pages

The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized separately mimicking the treatment of full loop quantum gravity. The new quantum dynamics for the spatially flat Friedmann-Robertson-Walker model with a massless scalar field as an emergent time is studied. By semiclassical analysis, the effective Hamiltonian constraint is obtained, which indicates that the new quantum dynamics has the correct classical limit. The classical big-bang singularity is again replaced by a quantum bounce. Similar to the case of quantizing only the Euclidean term, the backward evolution of the cosmological model determined by the new effective Hamiltonian will be bounced to an asymptotic de Sitter universe coupled to a massless scalar field, while the problem of negative energy density of matter in the former case is resolved., Comment: 12 pages, 5 figures

The Hamiltonian formulation of the lowest-order projectable Horava gravity, namely the so-called $\lambda$-$R$ gravity, is studied. Since a preferred foliation has been chosen in projectable Horava gravity, there is no local Hamiltonian constraint in the theory. In contrast to general relativity, the constraint algebra of $\lambda$-$R$ gravity forms a Lie algebra. By canonical transformations, we further obtain the connection-dynamical formalism of the $\lambda$-R gravity theories with real $su(2)$-connections as configuration variables. This formalism enables us to extend the scheme of non-perturbative loop quantum gravity to the $\lambda$-$R$ gravity. While the quantum kinematical framework is the same as that for general relativity, the Hamiltonian constraint operator of loop quantum $\lambda$-$R$ gravity can be well defined in the diffeomorphism-invariant Hilbert space. Moreover, by introducing a global dust degree of freedom to represent a dynamical time, a physical Hamiltonian operator with respect to the dust can be defined and the physical states satisfying all the constraints are obtained., Comment: 8 pages, published version for PRD

There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the literature, we check their consistency by the graphical calculus. Our calculation based on the original Brink graphical method is obviously simpler than the algebraic calculation. It turns out that our consistency check fixes the regulating factor $\kappa_{\rm reg}$ of the Ashtekar-Lewandowski volume operator as $\frac12$, which corrects its previous value in the literature., Comment: 12 pages, 4 figures; minor updates

In this paper, a new Hamiltonian constraint operator for loop quantum cosmology is constructed by using the Chern-Simons action. The quantum dynamics of the $k=0$ cosmological model with respect to a massless scalar field as an emergent time is determined by a difference equation. The semiclassical analysis shows that the new quantum dynamics has the correct classical limit, and the classical big-bang singularity is again replaced by the quantum bounce. Interestingly, the inverse time evolution of the flat Friedmann-Robertson-Walker cosmological model determined by the effective Hamiltonian will be bounced to an asymptotic de Sitter universe., Comment: 8 pages, 2 figures; version published in PRD