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A causal analysis of ground-level ozone, meteorological factors, and other air pollutants: an in-depth AI-based study applied to the climate of Craiova City, Romania 地面臭氧、气象因素和其他空气污染物的因果分析:一项应用于罗马尼亚克拉约瓦市气候的深度人工智能研究
IF 2.9 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2026-03-12 DOI: 10.1140/epjp/s13360-026-07495-x
Youness El Mghouchi, Mihaela Tinca Udristioiu

Ground-level ozone is a major air pollutant whose concentrations are influenced by meteorological conditions and other air pollutants. Understanding the causal relationships among ozone, meteorological variables, and other air pollutants is important for two reasons: (1) accurate prediction and forecasting and (2) effective air quality management. This study employs a combination of Granger causality testing, cross-correlation analysis, multiple linear regression, deep NARMAX modelling, and structural equation modelling to investigate the causal and time-lagged effects of meteorological and anthropogenic factors on ozone formation and depletion. A five-year dataset of hourly measurements of ozone, other air pollutants, and meteorological parameters is analysed for Craiova, Romania, to identify the dominant drivers of ozone variability. The results provide a basis for developing improved predictive models and offer insights into the delayed effects of air pollutants and weather conditions on urban ground-level ozone concentrations, supporting informed strategies for air quality management.

地面臭氧是一种主要的空气污染物,其浓度受气象条件和其他空气污染物的影响。了解臭氧、气象变量和其他空气污染物之间的因果关系有两个重要原因:(1)准确的预测和预报;(2)有效的空气质量管理。本研究采用格兰杰因果检验、互相关分析、多元线性回归、深度NARMAX模型和结构方程模型相结合的方法,探讨了气象因子和人为因子对臭氧形成和消耗的因果效应和滞后效应。在罗马尼亚的Craiova分析了一个每小时测量臭氧、其他空气污染物和气象参数的五年数据集,以确定臭氧变率的主要驱动因素。这些结果为开发改进的预测模型提供了基础,并为空气污染物和天气条件对城市地面臭氧浓度的延迟效应提供了见解,为空气质量管理的知情策略提供了支持。
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引用次数: 0
The bound orbits and gravitational waveforms of timelike particles around renormalization group improved Kerr black holes 重整化群周围类时粒子的束缚轨道和引力波形改进了克尔黑洞
IF 4.8 2区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Pub Date : 2026-03-12 DOI: 10.1140/epjc/s10052-026-15510-9
Yong-Zhuang Li, Xiao-Mei Kuang

In this article, we investigate the bound orbits of the timelike particles and the gravitational waveforms emitted from these orbits around a renormalization group improved Kerr black hole in the framework of the asymptotic safety approach. The running Newton coupling in the metric is characterized by two free quantum parameters ((omega ,,gamma )) arising from the non-perturbative renormalization group theory and the appropriate cutoff identification, respectively. As expected, the radii of the horizon, the marginally bound orbits and the innermost stable orbit are all decrease as the quantum parameters increase. Under the extreme mass-ratio inspirals approximation the deviation of gravitational waveforms radiated by the periodic orbits from those in the classical Kerr background increases with the two quantum parameters. However, this effect is much smaller in the retrograde case compared to the prograde case. Especially, by comparing the characteristic strain of those gravitational wave with the sensitivity curve of several potential detectors, we find that their characteristic frequencies can fall within the sensitivity ranges of several planned gravitational wave observatories, suggesting that such signals may be detectable with sufficient instrumental sensitivity.

本文在渐近安全方法的框架下,研究了类时粒子围绕改进Kerr黑洞的束缚轨道和这些轨道发出的引力波。度量中的运行牛顿耦合由两个自由量子参数((omega ,,gamma ))表征,分别由非摄动重整化群论和适当的截止识别产生。正如预期的那样,视界半径、边缘束缚轨道半径和最内层稳定轨道半径都随着量子参数的增大而减小。在极端质量比吸气近似下,周期轨道辐射的引力波与经典克尔背景下的引力波的偏差随着两个量子参数的增大而增大。然而,与进展病例相比,逆行病例的这种影响要小得多。特别是,通过将这些引力波的特征应变与几个潜在探测器的灵敏度曲线进行比较,我们发现它们的特征频率可以落在几个计划的引力波天文台的灵敏度范围内,这表明这些信号可以用足够的仪器灵敏度检测到。
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引用次数: 0
Studying the relationship between microparticle properties and manipulation performance of swirl microfluidic chip 研究了涡流微流控芯片的微粒特性与操纵性能的关系
IF 2.9 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2026-03-12 DOI: 10.1140/epjp/s13360-026-07478-y
Yanping Dang, Qin Zhang, Jiaming Huang

Microfluidics technology, as an emerging method for cell/microparticle manipulation, offers advantages such as low cost, simplicity, and high efficiency. In previous research, we developed multi-channel swirl microfluidic chips that enabled various manipulation functions, including particle capture, transfer, assembly, sorting, and enrichment. To achieve more precise control of microparticle, this paper investigates the relationship between microparticle’s physical properties and manipulation performance based on a two-microchannel swirl microfluidic chip. First, we conduct physical mechanisms analysis to reveal the force applied to microparticle in a swirl. We analyze the correlation between microparticle parameters and manipulation performance, specifically the capture time and post-capture angular velocity. Additionally, we establish a predictive model between these variables. The results show that the model can achieve bidirectional predictions between microparticle property and manipulation performance, with a mean squared error of less than 0.01. This study introduces data-driven to enrich the traditional approaches of microfluidic chips for particle manipulation and analysis. The results provide guidance for advanced microfluidic chips.

Graphical Abstract

This paper investigates the relationship between microparticle’s physical properties and manipulation performance based on a two-microchannel swirl microfluidic chip. We analyzed the correlation between particle parameters and their manipulation performance, specifically the capture time and post-capture rotational angular velocity. This study introduces data-driven and machine learning, enriching the traditional approaches of microfluidic chips for particle manipulation and analysis. The results provide guidance for manipulating particles in microfluidic chips and offer valuable insights for future applications in biosensors, biomedicine, and chemistry research.

微流体技术作为一种新兴的细胞/微粒操作方法,具有成本低、操作简单、效率高等优点。在之前的研究中,我们开发了多通道涡流微流控芯片,实现了多种操作功能,包括粒子捕获、转移、组装、分选和富集。为了实现对微颗粒的更精确控制,本文基于双微通道旋流微流控芯片,研究了微颗粒的物理特性与操作性能之间的关系。首先,我们进行了物理机制分析,揭示了在涡流中施加在微粒上的力。我们分析了微粒参数与操作性能之间的关系,特别是捕获时间和捕获后的角速度。此外,我们建立了这些变量之间的预测模型。结果表明,该模型可以实现微粒特性与操作性能之间的双向预测,均方误差小于0.01。本研究引入数据驱动,丰富了传统的微流控芯片的颗粒操作和分析方法。研究结果对开发新型微流控芯片具有指导意义。摘要基于双微通道旋流微流控芯片,研究了微颗粒的物理性质与操作性能之间的关系。我们分析了粒子参数与其操纵性能之间的关系,特别是捕获时间和捕获后的旋转角速度。本研究引入数据驱动和机器学习,丰富了传统的微流控芯片的颗粒操作和分析方法。研究结果为微流控芯片的颗粒操纵提供了指导,并为未来在生物传感器、生物医学和化学研究中的应用提供了有价值的见解。
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引用次数: 0
Observability of gravitational waves excited by binary stars orbiting around a supermassive black hole by space-based gravitational wave observatory 天基引力波天文台对围绕超大质量黑洞运行的双星激发的引力波的可观测性
IF 4.8 2区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Pub Date : 2026-03-12 DOI: 10.1140/epjc/s10052-026-15455-z
Kun Meng, Hongsheng Zhang, Xi-Long Fan, Yong Yuan, Fei Du

We produce the gravitational waveforms for the extreme mass ratio inspiral systems (EMRIs) of binary stars moving around central supermassive black hole (SBH), or called B-EMRIs. We calculate the external orbits of the binary stars via the commonly used Hamilton–Jacobi (HJ) approach, and calculate the internal orbits of the binary stars via Lagrangican approach. To improve accuracy we adopt the quadrupole-octupole expression of gravitational wave (GW) and study the contribution of radiation reaction. Compared to the waveforms of EMRIs, there are higher frequency oscillations superposed on the waveforms of B-EMRIs. We perform frequency spectrum analysis of the GW waveforms, and find that higher frequency signals give their prominency in the waveforms of B-EMRIs. To obtain high precise result for future observation of GWs from space-based detector, we take into account gravito-electromagnetic (GEM) force, and compare the waveforms of B-EMRIs with GEM effects against those of B-EMRIs without GEM effects and against those of EMRIs. The result of mismatch shows that the waveforms of B-EMRIs are credibly distinguishable by the space-based GW detectors when GEM force is considered.

我们为围绕中心超大质量黑洞(SBH)或称为B-EMRIs的双星运动的极端质量比吸气系统(EMRIs)产生重力波形。我们用常用的哈密顿-雅可比(HJ)方法计算了双星的外轨道,用拉格朗日方法计算了双星的内轨道。为了提高引力波的精度,我们采用了四极-八极的引力波表达式,并研究了辐射反应的贡献。与emri的波形相比,b - emri的波形上叠加了更高频率的振荡。我们对GW波形进行了频谱分析,发现高频信号在B-EMRIs波形中表现突出。为了获得更高精度的天基探测器GWs观测结果,我们考虑了重力电磁(GEM)力,并将具有GEM效应的B-EMRIs与不具有GEM效应的B-EMRIs以及EMRIs的波形进行了比较。失配结果表明,在考虑GEM力的情况下,天基GW探测器可以很好地分辨出B-EMRIs的波形。
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引用次数: 0
Evolution of innermost stable circular orbit and light ring of a charged black hole induced by the scalarization 标化诱导带电黑洞最内层稳定圆轨道和光环的演化
IF 4.8 2区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Pub Date : 2026-03-12 DOI: 10.1140/epjc/s10052-026-15500-x
Yu-Peng Zhang, Shao-Wen Wei, Yu-Xiao Liu

In this paper, we investigate the dynamical evolution of the innermost stable circular orbit and light ring of a charged black hole under the influence of scalarization dynamics. This is achieved through a series of nonlinear simulations within the framework of the Einstein–Maxwell-dilaton theory. By combining these nonlinear simulations with a (3+1) approach to geodesics in the dynamical spacetime, we derive the conditions for determining the ISCO and light ring in such a dynamical spacetime. Our results demonstrate how the ISCO and light ring evolve as a ‘hairless’ charged black hole transitions to a scalarized state. Moreover, we find that black hole scalarization leads to an increase in the areal radii of both the ISCO and light ring. These findings provide new insights into black hole scalarization, particularly concerning the dynamical evolution of the ISCO and light ring in a dynamically evolving spacetime.

本文研究了标量动力学影响下带电黑洞最内层稳定圆轨道和光环的动力学演化。这是通过在爱因斯坦-麦克斯韦膨胀理论框架内的一系列非线性模拟来实现的。通过将这些非线性模拟与动态时空中测地线的(3+1)方法相结合,我们推导出了在这种动态时空中确定ISCO和光环的条件。我们的研究结果展示了ISCO和光环是如何随着“无毛”带电黑洞向标化状态的转变而演变的。此外,我们发现黑洞标化导致ISCO和光环的面半径增加。这些发现为黑洞尺度化提供了新的见解,特别是在动态演化的时空中ISCO和光环的动态演化。
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引用次数: 0
A two-dimensional chaotic map with non-equidistant initial value offset boosting characteristics and its application in image encryption 具有非等距初值偏移增强特性的二维混沌映射及其在图像加密中的应用
IF 2.9 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2026-03-12 DOI: 10.1140/epjp/s13360-026-07461-7
Xili Zhang, Anke Liuli, Zean Tian, Qiao Wang, Xinghui Chen, Xin Peng, Kai Zeng, Qingqing He

Owing to their unique nonlinear dynamical characteristics, discrete memristive chaotic systems have received extensive attention in recent years. In this study, a two-dimensional discrete memristive chaotic system with non-equidistant initial value offset boosting characteristics (2D-NDMS) is constructed, and its dynamical distribution and spectral entropy complexity are systematically analyzed. The study finds that in the process of increasing the offset of initial values, the system exhibits alternating offsets between two non-equidistant regions, accompanied by local abnormal offset behavior during region switching. Further analysis of the system's evolution from transient chaos to steady state reveals the existence of dual-channel transient chaotic paths, which eventually converge to the same non-connected stable attractor. In terms of engineering applications, this study implements the chaotic attractor of the system on the STM32 hardware platform and applies it to the design of a pseudorandom number generator, with the generated sequences passing the NIST tests. Furthermore, the system is applied to image encryption, and the security of the encryption system is evaluated from multiple perspectives.

离散记忆混沌系统由于其独特的非线性动力学特性,近年来受到了广泛的关注。本文构造了一个具有非等距初值偏移升压特性的二维离散记忆性混沌系统(2D-NDMS),系统地分析了其动力学分布和谱熵复杂度。研究发现,在增加初始值偏移量的过程中,系统在两个非等距区域之间出现交替偏移,并伴随着区域切换时的局部异常偏移行为。进一步分析了系统从瞬态混沌到稳态的演化过程,发现存在双通道瞬态混沌路径,最终收敛到相同的非连通稳定吸引子。在工程应用方面,本研究在STM32硬件平台上实现了系统的混沌吸引子,并将其应用于伪随机数生成器的设计中,生成的序列通过了NIST测试。并将该系统应用于图像加密,从多个角度对加密系统的安全性进行了评价。
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引用次数: 0
Quantum discord: as a measure of quantumness of correlation between superposed non-degenerate three-level laser and suharmonic cavity light beams 量子不和谐:作为叠加非简并三能级激光与超调和腔光束之间相关量子量的度量
IF 2 3区 物理与天体物理 Q3 OPTICS Pub Date : 2026-03-12 DOI: 10.1007/s00340-026-08654-9
Menwuyelet Melaku Folla, Deribe Hirpo Aredo

This research offers a thorough analysis of the non-classical features associated with cavity radiation produced by a combination of superposed non-degenerate three-level lasers and non-degenerate subharmonic light beams. The Q-functions of the individual light beams are utilized to derive the Q-function for the superposed cavity radiation. From this derived Q-function, we analyze the expectation values of operators. Using the relevant expectation values (correlations) of these operators, we calculate the quantum discord for the superposed cavity light beams being studied. The results indicate that quantum discord increases with the linear gain coefficient and atomic coherence, while it decreases with the parameter (gamma ) and population inversion, (xi ). Although the trends of forward and backward quantum discord are generally similar, it is distinctly observed that the forward quantum discord is consistently less than the backward quantum discord. The variation in quantum discord observed in the forward and reverse processes is primarily linked to the differences in the mean photon numbers of mode-a and mode-b within the non-degenerate three-level laser system. Additionally, a juxtaposition of quantum discord with entanglement, evaluated through the Logarithmic Negativity criterion, reveals that the quantum discord associated with the superposed cavity radiation remains above the Logarithmic Negativity level. Nonetheless, for certain values of (gamma ) exceeding 0.3, quantum discord may fall below the Logarithmic Negativity threshold. This observation underscores the notion that quantum discord is a significant aspect of entanglement. Through the application of quantum discord and the Logarithmic Negativity criterion, it is established that the superposed non-degenerate cavity radiation manifests quantum properties and entanglement.

本研究对叠加非简并三能级激光与非简并次谐波光束组合产生的腔辐射的非经典特征进行了深入分析。利用单个光束的q函数推导出叠加腔辐射的q函数。从这个导出的q函数,我们分析了算子的期望值。利用这些算子的相关期望值(相关性),我们计算了所研究的叠加腔光束的量子不谐。结果表明,量子不和谐随线性增益系数和原子相干度的增加而增加,随参数(gamma )和居数反转(xi )的增加而减小。虽然前向和后向量子不和谐的趋势大致相似,但可以清楚地观察到,前向量子不和谐始终小于后向量子不和谐。在非简并三能级激光系统中,正反过程中观测到的量子不和谐的变化主要与模a和模b的平均光子数的差异有关。此外,通过对数负性标准评估量子不和谐与纠缠的并置,揭示了与叠加腔辐射相关的量子不和谐仍然高于对数负性水平。然而,对于(gamma )超过0.3的某些值,量子不和谐可能低于对数负性阈值。这一观察结果强调了量子不和谐是纠缠的一个重要方面。通过应用量子失谐和对数负性判据,证明了叠加的非简并腔辐射具有量子特性和纠缠态。
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引用次数: 0
Double-layered vacuum bubbles and cosmological phase transitions 双层真空气泡与宇宙相变
IF 4.8 2区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Pub Date : 2026-03-12 DOI: 10.1140/epjc/s10052-026-15512-7
Dongdong Wei, Zong-Kuan Guo, Qiqi Fan

We investigate the evolution and formation of double-layered vacuum bubbles during cosmological phase transitions with multiple vacua. We employ lattice simulations to show that flyover transitions can produce double-layered vacuum bubbles by overcoming successive potential barriers, thereby suggesting a novel bubble vacuum configuration in cosmological phase transitions. The evolution of these bubbles, including wall acceleration, collisions, and the formation of trapped regions, is explored through numerical simulations. Our results show that the dynamics of double-layered bubbles differ significantly from standard single-wall bubbles, with implications for cosmological observables such as gravitational wave production and baryogenesis.

我们研究了多重真空的宇宙相变过程中双层真空气泡的演化和形成。我们利用晶格模拟表明,立交桥跃迁可以通过克服连续的势垒产生双层真空气泡,从而提出了一种新的宇宙相变气泡真空构型。这些气泡的演化,包括壁加速,碰撞,以及被困区域的形成,通过数值模拟进行了探索。我们的研究结果表明,双层气泡的动力学与标准的单壁气泡有很大的不同,这对引力波产生和重子生成等宇宙学观测结果有影响。
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引用次数: 0
A search for (B_{s0}^{*}) and (B^{*}_{s1}) through the (K^{-}p) interaction 通过(K^{-}p)交互搜索(B_{s0}^{*})和(B^{*}_{s1})
IF 4.8 2区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Pub Date : 2026-03-12 DOI: 10.1140/epjc/s10052-026-15495-5
Min Yuan, Yin Huang

Studying heavy-quark hadrons is crucial due to the nonperturbative nature of low-energy QCD, with Heavy-Quark Symmetry (HQS) serving as a key framework for understanding their spin and flavor symmetries. However, a key issue is that the theoretically expected (B^{(*)}bar{K}) molecular states have not yet been observed, although they are considered the bottom-quark counterparts of the observed (bar{D}^{(*)}bar{K}) molecular states (corresponding to (D_{s0}(2317/2460)^{-})), which challenges the universality of HQS. The main goal of this work is to search for the theoretically predicted (Bbar{K}) and (B^{*}bar{K}) molecular states, namely (B_{s0}^{*}(5725)) and (B_{s1}^{*}(5778)), via the reactions (K^{-}p rightarrow varLambda _{b}^{0} B_{s0}^{*}) and (K^{-}p rightarrow varLambda _{b}^{0} B_{s1}^{*}). Within an effective Lagrangian framework, we compute the relevant cross sections, considering t-channel (B^{(*)}) exchanges and (K^{-}p) initial-state interactions (ISI). The results show that the production cross sections of (B_{s0}^{*}(5725)) and (B_{s1}^{*}(5778)) can reach the order of 0.01 nb, and we suggest that experiments searching for (B_{s0}^{*}(5725)) are best performed at (P_{K^{-}} = 12.18~textrm{GeV}), while higher energies are most favorable for producing (B_{s1}^{*}(5778)). The ISI play a crucial role, as they not only significantly enhance the production cross sections of (B_{s0}^{*}(5725)) and (B_{s1}^{*}(5778)) (by roughly one order of magnitude) but also markedly affect the angular distributions of the produced particles. We also calculated the production cross sections of the conventional quark–antiquark states (B_{s0}^*(5700)) and (B_{s1}^*(5720)), which are found to be nearly the same as those of (B_{s0}^{*}(5725)) and (B_{s1}^{*}(5778)). Although their internal structures remain ambiguous, these results can inform future experimental searches at CERN and J-PARC.

研究重夸克强子由于低能QCD的非微扰性质是至关重要的,而重夸克对称性(HQS)是理解其自旋和味道对称性的关键框架。然而,一个关键的问题是,理论上预期的(B^{(*)}bar{K})分子状态尚未被观察到,尽管它们被认为是观察到的(bar{D}^{(*)}bar{K})分子状态(对应于(D_{s0}(2317/2460)^{-}))的底夸克对偶,这对HQS的普遍性提出了挑战。本工作的主要目标是通过反应(K^{-}p rightarrow varLambda _{b}^{0} B_{s0}^{*})和(K^{-}p rightarrow varLambda _{b}^{0} B_{s1}^{*})寻找理论预测的(Bbar{K})和(B^{*}bar{K})分子状态,即(B_{s0}^{*}(5725))和(B_{s1}^{*}(5778))。在一个有效的拉格朗日框架内,我们计算了相关的横截面,考虑了t通道(B^{(*)})交换和(K^{-}p)初始状态相互作用(ISI)。结果表明,(B_{s0}^{*}(5725))和(B_{s1}^{*}(5778))的生成截面可以达到0.01 nb的量级,我们建议在(P_{K^{-}} = 12.18~textrm{GeV})处进行寻找(B_{s0}^{*}(5725))的实验最好,而更高的能量最有利于生成(B_{s1}^{*}(5778))。ISI起着至关重要的作用,因为它们不仅显著提高了(B_{s0}^{*}(5725))和(B_{s1}^{*}(5778))的生产截面(大约提高了一个数量级),而且显著影响了所生产颗粒的角分布。我们还计算了常规夸克-反夸克态(B_{s0}^*(5700))和(B_{s1}^*(5720))的产生截面,发现它们与(B_{s0}^{*}(5725))和(B_{s1}^{*}(5778))的产生截面几乎相同。尽管它们的内部结构仍然不明确,但这些结果可以为CERN和J-PARC未来的实验搜索提供信息。
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引用次数: 0
Third type of spacetime with the coexistence of integrability and non-integrability 第三种可积性与不可积性并存的时空
IF 4.8 2区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Pub Date : 2026-03-12 DOI: 10.1140/epjc/s10052-026-15482-w
Junjie Lu, Xin Wu

The integrability or non-integrability of a spacetime usually refers to whether the motion of massive or massless particles in the spacetime is integrable or not. The standard black hole spacetimes such as the Schwarzschild and Kerr metrics are always integrable for both timelike and null geodesics. They belong to a first type of spacetime. However, the Melvin type spacetimes as a second type of spacetime are non-integrable, regardless of whether they are for massive or massless particle motion. In this paper, we discover the possibility of a third type of spacetime with non-integrable dynamics of timelike geodesics and integrable dynamics of null geodesics. In fact, conformal transformations may transform type one solutions into type three. This is due to the conformal factors preventing the separation of variables from the Hamilton–Jacobi equation and leading to the absence of a fourth constant of motion for the massive particle dynamics. Nevertheless, the massless particle motion still remains integrable in these metrics for any conformal factors because the conformal factors have no effect on the null geodesics whatsoever. The conformal Kerr metric is an example of the third type of spacetime. In addition to the conformal transformation method, other paths may yield the third type of spacetime. The Kerr–Bertotti–Robinson black hole metric and the accelerating Schwarzschild spacetime are two examples of non-conformal solutions that are also of type three.

时空的可积性或不可积性通常是指有质量粒子或无质量粒子在时空中的运动是否可积。标准黑洞时空,如史瓦西和克尔度规,对于类时测地线和零测地线总是可积的。它们属于第一种时空。然而,作为第二种时空的梅尔文型时空是不可积的,无论它们是针对有质量的还是无质量的粒子运动。在本文中,我们发现了具有类时测地线不可积动力学和零测地线可积动力学的第三类时空的可能性。事实上,保角变换可以将第一类解转换为第三类解。这是由于保形因子阻止了从Hamilton-Jacobi方程中分离变量,导致大质量粒子动力学中缺少第四个运动常数。然而,对于任何保形因子,无质量粒子运动在这些度量中仍然是可积的,因为保形因子对零测地线没有任何影响。共形克尔度规是第三种时空的一个例子。除了保角变换方法之外,其他路径也可能产生第三种时空。kerr - bertoti - robinson黑洞度规和加速史瓦西时空是非共形解的两个例子,也是第三类。
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引用次数: 0
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