Physics of the Dark Universe最新文献_第4页

F-mode oscillations of neutron stars with dark matter from neutron decay: Implications for gravitational-wave detectability 中子衰变中含有暗物质的中子星的f模振荡：引力波可探测性的含义

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-30 DOI: 10.1016/j.dark.2025.102208

Wasif Husain

In this study, the impact of neutron decay into dark matter and various dark matter self-interaction strengths on neutron star properties have been explored. Using the quark-meson coupling (QMC) model for nucleon-only equations of state (EoSs), the effects of different matter compositions have been compared, including strange matter and self-interacting dark matter. The results demonstrate that increasing DM-DM self-repulsion stiffens the EoS, influencing the mass-radius relationship and stability of neutron stars. Furthermore, fundamental mode (f-mode) oscillations have been analyzed, which serve as a diagnostic tool for probing neutron star interiors. The f-mode frequencies follow universal relations, reinforcing their applicability for constraining dense matter properties. It has been shown that neutron stars composed of nucleons-only and self-interacting dark matter exhibit a universal behavior in damping time and angular frequency, whereas strange matter and non-self-interacting dark matter deviate from this trend. Importantly, it has been shown that for a GW energy release of E ∼ 10⁵² erg and a source distance of 25 Mpc, the characteristic strain and signal-to-noise ratio exceed the ET-D sensitivity threshold below  ∼ 2.1 kHz for all models except the non-interacting DM case, demonstrating that neutron-to-dark matter decay scenarios, including the role of DM self-interactions, can be tested through next-generation gravitational-wave asteroseismology, offering a new probe of DM physics and the neutron lifetime anomaly.

本研究探讨了中子衰变为暗物质和各种暗物质自相互作用强度对中子星性质的影响。利用纯核子状态方程的夸克-介子耦合（QMC）模型，比较了不同物质组成的影响，包括奇异物质和自相互作用暗物质。结果表明，DM-DM自斥力的增加使EoS变硬，影响中子星的质量-半径关系和稳定性。此外，还分析了基模（f模）振荡，它可以作为探测中子星内部的诊断工具。f模频率遵循普遍关系，加强了它们在约束致密物质性质方面的适用性。研究表明，由纯核子暗物质和自相互作用暗物质组成的中子星在衰减时间和角频率上表现出普遍的行为，而奇异物质和非自相互作用暗物质则偏离这一趋势。重要的是，研究表明，对于E ~ 1052 erg的GW能量释放和25 Mpc的源距离，除了非相互作用的DM情况外，所有模型的特征应力和信噪比都超过了ET-D灵敏度阈值，低于 ~ 2.1 kHz，这表明中子到暗物质的衰变情景，包括DM自相互作用的作用，可以通过下一代引力波星震学进行测试。提供了DM物理和中子寿命异常的新探索。

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引用次数: 0

Generalized free energy landscapes from Iyer-Wald formalism 从yer- wald形式论出发的广义自由能景观

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-30 DOI: 10.1016/j.dark.2025.102210

Shan-Ping Wu , Yu-Xiao Liu , Shao-Wen Wei

The generalized free energy landscape plays a pivotal role in understanding black hole thermodynamics and phase transitions. In general relativity, one can directly derive the generalized free energy from the contributions of black holes exhibiting conical singularities. In this work, we extend this idea to general covariant theories. By employing Noether’s second theorem, we present an alternative formulation of the Lagrangian, which can elucidate the role of conical singularities. We demonstrate that, in general, the contribution from conical singularities depends on the specific implementation of the regularization scheme and is not uniquely determined; this feature is explicitly exhibited and confirmed in three-dimensional new massive gravity. Nevertheless, these ambiguities can be absorbed into the second-order (and higher) corrections induced by conical singularities when the gravitational theory is described by the Lagrangian L(g_ab, R_abcd). Moreover, for certain theories such as general relativity and Bumblebee gravity, this contribution simplifies to a well-defined result. However, the interpretation of the generalized free energy in Bumblebee gravity is somewhat different, with its extrema corresponding to the geometry of conical singularities. Our results uncover the particular properties of the generalized free energy beyond general relativity.

广义自由能景观在理解黑洞热力学和相变方面起着关键作用。在广义相对论中，人们可以直接从具有锥形奇点的黑洞的贡献中推导出广义自由能。在这项工作中，我们将这一思想推广到一般协变理论。利用诺特第二定理，我们给出了拉格朗日的另一种表述，它可以阐明圆锥奇点的作用。我们证明，在一般情况下，锥奇点的贡献取决于正则化方案的具体实现，并不是唯一确定的；这一特征在三维新质量引力中得到了明确的展示和证实。然而，当拉格朗日L（gab, Rabcd）描述引力理论时，这些模糊性可以被吸收到由锥形奇点引起的二阶（或更高阶）修正中。此外，对于某些理论，如广义相对论和大黄蜂引力，这一贡献简化为一个定义良好的结果。然而，对大黄蜂引力中广义自由能的解释有些不同，其极值对应于圆锥奇点的几何形状。我们的结果揭示了广义自由能超越广义相对论的特殊性质。

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引用次数: 0

Analytic and numerical constraints on QPOs in EHT and XRB sources using quantum-corrected black holes 基于量子修正黑洞的EHT和XRB源QPOs的解析和数值约束

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-29 DOI: 10.1016/j.dark.2025.102206

Ahmad Al-Badawi , Faizuddin Ahmed , Orhan Dönmez , Fatih Doğan , Behnam Pourhassan , i̇zzet Sakallı , Yassine Sekhmani

This investigation examines quasi-periodic oscillations (QPOs) in two quantum-corrected black hole (BH) spacetimes that preserve general covariance while incorporating quantum gravitational effects through a dimensionless parameter ζ. We combine analytical derivations of epicyclic frequencies with comprehensive numerical simulations of Bondi-Hoyle-Lyttleton (BHL) accretion to explore how quantum corrections manifest in observable astrophysical phenomena. Using a fiducial BH mass of

M = 10 M_{⊙}

representative of stellar-mass X-ray binaries, we demonstrate that the two models exhibit fundamentally different behaviors: Model-I modifies both temporal and radial metric components, leading to innermost stable circular orbit migration proportional to ζ⁴ and dramatic stagnation point evolution from 27M to 5M as quantum corrections strengthen. Model-II preserves the classical temporal component while altering only spatial geometry, maintaining constant stagnation points and stable cavity structures throughout the parameter range. Our numerical simulations reveal distinct QPO generation mechanisms, with Model-I showing systematic frequency evolution and cavity shrinkage that suppresses oscillations for ζ ≥ 3M, while Model-II maintains stable low-frequency modes up to ζ ≥ 5M. Power spectral density analyzes demonstrate characteristic frequency ratios (3: 2, 2: 1, 5: 3) consistent with observations from X-ray binaries, providing specific targets for discriminating between quantum correction scenarios. The hydrodynamically derived constraints (ζ ≲ 4M) show remarkable agreement with independent Event Horizon Telescope limits for M87* and Sgr A*, validating our theoretical framework through multiple observational channels. These results establish QPO frequency analysis as a probe for detecting quantum gravitational effects in astrophysical BHs and demonstrate the complementary nature of timing and imaging observations in constraining fundamental physics.

本研究考察了两个量子校正黑洞（BH）时空中的准周期振荡（QPOs），这些时空保持了一般协方差，同时通过无量纲参数ζ结合了量子引力效应。我们将行星周期频率的解析推导与Bondi-Hoyle-Lyttleton （BHL）吸积的综合数值模拟结合起来，探索量子修正如何在可观测的天体物理现象中表现出来。利用代表恒星质量x射线双星的基准黑洞质量M=10M⊙，我们证明了这两个模型表现出根本不同的行为：模型1修改了时间和径向度量分量，导致最内层稳定的圆轨道偏移与ζ4成比例，并且随着量子修正的加强，从27M到5M的急剧停滞点演化。模型ii保留了经典的时间分量，同时只改变了空间几何形状，在整个参数范围内保持恒定的驻点和稳定的空腔结构。我们的数值模拟揭示了不同的QPO产生机制，模型- 1显示系统的频率演化和空腔收缩，抑制ζ ≥ 3M的振荡，而模型- ii保持稳定的低频模式，直至ζ ≥ 5M。功率谱密度分析表明，特征频率比（3:2、2:1、5:3）与x射线双星观测结果一致，为区分量子校正场景提供了具体目标。流体动力学推导的约束（ζ ≤ 4M）与M87*和Sgr A*的独立事件视界望远镜极限具有显著的一致性，通过多个观测渠道验证了我们的理论框架。这些结果建立了QPO频率分析作为探测天体物理黑洞量子引力效应的探针，并证明了时序和成像观测在约束基础物理中的互补性。

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引用次数: 0

Growth index in the γδCDM model γ - δ cdm模型中的生长指数

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-25 DOI: 10.1016/j.dark.2025.102201

Cemsinan Deliduman , Furkan Şakir Dilsiz , Selinay Sude Binici

To better distinguish the nature of H₀ and S₈ tensions, it is necessary to separate the effects of expansion and the growth of structure. The growth index γ was identified as the most important parameter that characterizes the growth of density fluctuations independently of the effects of cosmic expansion. In the ΛCDM model, analyses performed with various cosmological datasets indicate that the growth index has to be larger than its theoretically predicted value. Cosmological models based on f(R) gravity theories have scale-dependent growth indices, whose values are even more at odds with the growth rate data. In this work, we evaluate the growth index in the γδCDM model both theoretically and numerically. Although based on f(R) gravity theory, we show through several analyses with different combinations of datasets that the growth index in the γδCDM model is very close in value to the ΛCDM and the ωCDM models. The growth of structure is suppressed in the γδCDM model, which is formulated with the extended gravitational growth framework. Upon analyzing cosmological data, we ascertain that the γδCDM model is equally competitive as the ΛCDM and the ωCDM models.

为了更好地区分H0和S8张力的性质，有必要将结构膨胀和生长的影响分开。生长指数γ被确定为最重要的参数，表征密度波动的增长独立于宇宙膨胀的影响。在ΛCDM模型中，对各种宇宙学数据集进行的分析表明，增长指数必须大于其理论预测值。基于f(R)引力理论的宇宙学模型具有依赖于尺度的增长指数，其值与增长率数据更加不一致。本文从理论和数值两方面对γ - δ cdm模型中的生长指数进行了评价。虽然基于f(R)引力理论，但我们通过对不同数据集组合的几种分析表明，γδCDM模型中的生长指数与ΛCDM和ωCDM模型的值非常接近。在扩展的重力生长框架下建立的γ - δ cdm模型中，结构的生长受到抑制。通过对宇宙学数据的分析，我们确定了γδCDM模型与ΛCDM和ωCDM模型具有同等的竞争力。

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引用次数: 0

Interior structure and physical features of dark energy relativistic stars in power law gravity model 幂律引力模型中暗能量相对论恒星的内部结构和物理特征

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-25 DOI: 10.1016/j.dark.2025.102198

M.R. Shahzad , Wajiha Habib , Asifa Ashraf , Muneerah Alomar , Awatef Abidi , Maryam Al Huwayz

The modeling of astrophysical compact objects has recently attracted significant interest of the research community to understand their stable internal structures. In particular, the addition of dark energy as another source of matter configuration in the interiors of such stars has elevated the focus on their theoretical development. In this study, we present a ne model of static, spherically symmetric, and anisotropic compact stars within the framework of f(R) modified theories. The stellar structure is described by a two-fluid system consisting of ordinary matter and dark energy. We develop the analytical solutions to the governing modified field equations using the well-known Finch-Skea ansatz for the metric potentials, coupled with a linear equation of state for the dark energy component. The model parameters, including the metric ansatz, are determined via smooth matching conditions at the boundary between the interior and exterior spacetime regions. To demonstrate the physical viability of the model, we apply our formulation to the compact star 4U 1538-52, utilizing the stable and widely studied

f (R) = R + 2 χ R^{2}

gravity model. We analyze an extensive investigation of the physical features, including the behavior of metric equations, matter variables, energy conditions, and stability criteria. In addition, we evaluate the evolution of the mass function, surface redshift, and compactness factor of the considered compact star candidates. The results confirm the stability, feasibility, and physical impact of the constructed solutions along with presenting additional insight into the interplay between dark energy structures and modified gravity within astrophysical circumstances. Graphical representations of key parameters enhance the clarity of our findings. The results demonstrate that our model is physically acceptable and stable in f(R) gravity.

天体物理致密物体的建模最近引起了研究界的极大兴趣，以了解它们稳定的内部结构。特别是，暗能量作为这类恒星内部物质结构的另一个来源的增加，提高了对它们理论发展的关注。在这项研究中，我们提出了一个在f(R)修正理论框架内的静态、球对称和各向异性致密恒星的新模型。恒星结构被描述为由普通物质和暗能量组成的双流体系统。我们利用著名的芬奇-斯基方差分析得到了控制修正场方程的解析解，并结合了暗能量分量的线性状态方程。模型参数，包括度量参数，通过内外时空区域边界的平滑匹配条件确定。为了证明该模型的物理可行性，我们利用稳定且广泛研究的f(R)=R+2χR2重力模型，将我们的公式应用于紧凑恒星4U 1538-52。我们分析了物理特征的广泛调查，包括度量方程的行为，物质变量，能量条件和稳定性标准。此外，我们评估了被考虑的紧致恒星候选者的质量函数、表面红移和紧致系数的演变。结果证实了构建的解决方案的稳定性、可行性和物理影响，同时对暗能量结构和天体物理环境下修正引力之间的相互作用提供了额外的见解。关键参数的图形表示增强了我们研究结果的清晰度。结果表明，该模型在f(R)重力下是物理上可接受的和稳定的。

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引用次数: 0

Quantum corrections and exotic criticality in charged rotating BTZ black holes 带电旋转BTZ黑洞中的量子修正和奇异临界

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-24 DOI: 10.1016/j.dark.2025.102202

Erdem Sucu, İzzet Sakallı

We investigate quantum corrections to the thermodynamics of charged, rotating BTZ black holes in AdS spacetime using both Generalized Uncertainty Principle (GUP) and exponential entropy corrections. The Hamilton–Jacobi tunneling method yields the Hawking temperature and its GUP-modified form, revealing how Planck-scale effects suppress thermal radiation. Exponential corrections to the Bekenstein-Hawking entropy lead to modified expressions for internal energy, Helmholtz and Gibbs free energies, pressure, enthalpy, and heat capacity. The AdS radius ℓ emerges as a critical parameter: smaller values enhance gravitational confinement and thermodynamic stability, while larger values weaken these effects. The heat capacity remains positive across parameter space, ruling out second-order phase transitions. However, the JT coefficient exhibits remarkable oscillatory behavior near r_h ≈ 1.05, alternating between heating and cooling phases during isenthalpic expansion. These oscillations intensify with increasing ℓ, indicating reduced stability in weakly curved AdS backgrounds. Gravitational redshift calculations in the weak-field limit show that the logarithmic charge coupling produces unbounded growth at large distances, with strong ℓ-dependence providing observational signatures. Our results demonstrate that (2+1)-dimensional black holes possess richer thermodynamic structure than their higher-dimensional counterparts, with quantum corrections introducing novel critical phenomena while preserving overall stability. These findings connect microscopic quantum gravity effects to macroscopic thermodynamic behavior, offering new perspectives on black hole physics in lower dimensions.

我们利用广义不确定性原理（GUP）和指数熵修正研究了AdS时空中带电旋转BTZ黑洞热力学的量子修正。Hamilton-Jacobi隧穿法产生了霍金温度及其修正后的gup形式，揭示了普朗克尺度效应是如何抑制热辐射的。对贝肯斯坦-霍金熵的指数修正导致了内能、亥姆霍兹和吉布斯自由能、压力、焓和热容的修正表达式。AdS半径作为一个关键参数出现：较小的值增强了引力约束和热力学稳定性，而较大的值则减弱了这些影响。热容在参数空间上保持正值，排除了二阶相变。然而，JT系数在rh ≈ 1.05附近表现出显著的振荡行为，在等焓膨胀过程中在加热阶段和冷却阶段之间交替。这些振荡随着r的增加而增强，表明弱弯曲AdS背景的稳定性降低。在弱场极限下的引力红移计算表明，对数电荷耦合在远距离上产生无界增长，具有强的依赖关系提供观测特征。我们的研究结果表明，（2+1）维黑洞比高维黑洞具有更丰富的热力学结构，量子修正在保持整体稳定性的同时引入了新的临界现象。这些发现将微观量子引力效应与宏观热力学行为联系起来，为较低维度的黑洞物理学提供了新的视角。

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引用次数: 0

Stability analysis and oscillatory behavior of orbits around Lorentz-violating black holes 违反洛伦兹黑洞轨道的稳定性分析和振荡行为

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-23 DOI: 10.1016/j.dark.2025.102200

Rana Muhammad Zulqarnain , Abdelmalek Bouzenada , Farruh Atamurotov , Ikhtiyor Saidov , A.S. Alqahtani , Phongpichit Channuie

In this paper, we investigate the motion of test particles around a black hole (BH) characterized by spontaneous Lorentz symmetry breaking, parameterized by α. We begin by outlining the theoretical framework underlying such BH geometries and subsequently analyze the corresponding dynamics of massive test particles. By applying the effective potential, we determine the exact conditions for circular trajectories and analyze the properties of the innermost stable circular orbits (ISCOs) parameters. In addition, the effective force acting on particles is studied, which gives further insight into orbital stability. Also, we are testing the BH shadow with M87* and Sgr A* under the influence of BH parameters.. Furthermore, we explore oscillatory phenomena associated with small perturbations around circular orbits, calculating the frequencies as measured by both local and distant observers, as well as the periastron precession. In this context, these results shed light on possible observational signatures of Lorentz-symmetry breaking in strong gravitational regimes and contribute to the understanding of modified BH physics.

本文研究了以自发洛伦兹对称破缺（α）为参数的黑洞周围测试粒子的运动。我们首先概述了这种黑洞几何形状的理论框架，随后分析了大质量测试粒子的相应动力学。利用有效势，我们确定了圆轨道的精确条件，并分析了最内层稳定圆轨道（ISCOs）参数的性质。此外，研究了作用在粒子上的有效作用力，对轨道稳定性有了进一步的认识。此外，我们还用M87*和Sgr A*在黑洞参数的影响下测试了黑洞阴影。此外，我们探索了与圆形轨道周围的小扰动相关的振荡现象，计算了由本地和远程观测者测量的频率，以及日冕进动。在这种背景下，这些结果揭示了在强引力条件下洛伦兹对称破缺的可能观测特征，并有助于理解修正的黑洞物理学。

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引用次数: 0

Novel solar system probes for primordial black holes 对原始黑洞的新型太阳系探测

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-21 DOI: 10.1016/j.dark.2025.102195

Oem Trivedi , Abraham Loeb

Primordial Black Holes (PBHs) represent one of the more interesting ways to address dark matter, at the interface of both cosmology and quantum gravity. It is no surprise then that testing PBHs is a venue of active interest, with several cosmological and astrophysical probes constraining different mass ranges. In this work, we propose novel Solar System scale searches for PBHs, motivated by the unique precision and coverage of local observables. We show that asteroid to dwarf planet mass PBHs can induce measurable dipolar timing signatures in pulsar timing arrays, while planetary mass PBHs can generate detectable ADAF accretion flares through interactions with Kuiper Belt bodies. Together, these complementary approaches open a new observational frontier for probing PBHs across mass ranges that remain unconstrained by conventional cosmological methods.

原始黑洞（PBHs）代表了一种更有趣的方式来解决暗物质，在宇宙学和量子引力的界面。毫无疑问，测试pbh是一个积极的兴趣点，有几个宇宙学和天体物理学探测器限制了不同的质量范围。在这项工作中，我们提出了新的太阳系尺度搜索pbh，动机是独特的精度和局部观测的覆盖范围。我们发现小行星到矮行星的质量pbh可以在脉冲星时序阵列中诱导可测量的偶极时序特征，而行星质量pbh可以通过与柯伊伯带天体的相互作用产生可检测的ADAF吸积耀斑。总之，这些互补的方法为探测不受传统宇宙学方法限制的质量范围内的pbh开辟了一个新的观测前沿。

引用次数: 0

Massive-photon electrodynamics and MHD in curved spacetime and cosmology 弯曲时空和宇宙学中的大质量光子电动力学和MHD

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-20 DOI: 10.1016/j.dark.2025.102192

Hyerim Noh , Jai-chan Hwang

We study a massive-photon electrodynamics and magnetohydrodynamics (MHD) in the curved spacetime of Einstein’s gravity. We consider a Proca-type photon mass and present equations in terms of electric and magnetic (EM) fields and the vector potential. We present the electrodynamics and MHD in the covariant and ADM formulations valid in general spacetime and in linearly perturbed cosmological spacetime. We present wave equations assuming the metric variations are negligible compared with the field variations. Equations are derived without fixing the temporal gauge condition and the gauge transformation properties of the EM fields and the vector potential are presented. Using the post-Newtonian approximation we show the dark Proca field behaves as dust in the non-relativistic limit under the Klein transformation.

研究了爱因斯坦引力下弯曲时空中的大质量光子电动力学和磁流体动力学。我们考虑了一个proca型光子质量，并给出了电磁场和矢量势的方程。我们提出了在一般时空和线性摄动宇宙学时空中有效的协变公式和ADM公式中的电动力学和MHD。我们提出波动方程，假设度规变化与场变化相比可以忽略不计。在不确定时间规范条件的情况下推导了方程，给出了电磁场和矢量势的规范变换性质。利用后牛顿近似，我们证明了在克莱因变换下的非相对论极限下，暗Proca场表现为尘埃。

引用次数: 0

Thermodynamic signatures of non-Abelian dilaton black holes 非阿贝尔膨胀黑洞的热力学特征

IF 6.4 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics of the Dark Universe

Pub Date : 2025-12-20 DOI: 10.1016/j.dark.2025.102197

Ankit Anand , Aditya Singh , Saeed Noori Gashti , Behnam Pourhassan

We investigate the thermodynamic extremality, topological charge structure, and thermodynamic curvature of non-Abelian dilaton black holes. The dilaton coupling significantly alters thermodynamic properties, enabling the verification of extremality conditions. By analyzing normalized thermodynamic vector fields, we classify topological charges through the identification of critical zero points, with their stability confirmed via winding number analysis. These topological sectors vary distinctly with the dilaton parameter. The free energy landscape is interpreted as a scalar field over parameter space, with its extrema corresponding to topological phases. This allows consistent charge assignments aligned with known solutions, such as the AdS Reissner-Nordström black hole. We further explore the topology of photon spheres and demonstrate their crucial role in black hole stability, establishing a strong link between thermodynamic topology and spacetime geometry. Finally, thermodynamic curvature is used to probe microscopic interactions, revealing predominantly attractive behavior with possible repulsive transitions near criticality. Our results indicate a rich phase structure and a non-trivial microstructure shaped by the interplay of dilaton and non-Abelian gauge fields.

研究了非阿贝尔膨胀黑洞的热力学极值性、拓扑电荷结构和热力学曲率。膨胀耦合显著地改变了热力学性质，使极端条件的验证成为可能。通过对归一化热力学向量场的分析，通过识别临界零点对拓扑电荷进行分类，并通过圈数分析确定拓扑电荷的稳定性。这些拓扑扇形随膨胀参数的变化而明显不同。自由能景观被解释为参数空间上的标量场，其极值对应于拓扑相。这使得电荷分配与已知的解决方案一致，例如AdS Reissner-Nordström黑洞。我们进一步探索了光子球的拓扑结构，并证明了它们在黑洞稳定性中的关键作用，建立了热力学拓扑和时空几何之间的紧密联系。最后，热力学曲率被用来探测微观相互作用，揭示了主要的吸引行为和可能的排斥转变接近临界。我们的结果表明，膨胀场和非阿贝尔规范场的相互作用形成了丰富的相结构和非平凡的微观结构。

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引用次数: 0