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Quantum geodesics reflecting the internal structure of stars composed of shells 反映由外壳组成的恒星内部结构的量子测地线
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-30 DOI: 10.1088/1475-7516/2024/07/089
Sojeong Cheong and Wontae Kim
In general relativity, an external observer cannot distinguish distinct internal structures between two spherically symmetric stars that have the same total mass M. However, when quantum corrections are taken into account, the external metrics of the stars will receive quantum corrections depending on their internal structures. In this paper, we obtain the quantum-corrected metrics at linear order in curvature for two spherically symmetric shells characterized by different internal structures: one with an empty interior and the other with N internal shells. The dependence on the internal structures in the corrected metrics tells us that geodesics on these backgrounds would be deformed according to the internal structures. We conduct numerical computations to find out the angle of geodesic precession and show that the presence of internal structures amplifies the precession angle reflecting the discrepancy between the radial and orbital periods within the geodesic orbit. The amount of the precession angle increases monotonically as the number of internal shells increases and it eventually converges to a certain value for N ⟶ ∞.
在广义相对论中,外部观察者无法区分两颗具有相同总质量 M 的球面对称恒星的不同内部结构。然而,当考虑到量子修正时,恒星的外部度量将根据其内部结构得到量子修正。在本文中,我们得到了两个内部结构不同的球面对称壳体(一个内部是空的,另一个内部有 N 个壳体)的曲率线性阶量子修正度量。修正度量对内部结构的依赖告诉我们,这些背景上的大地线会根据内部结构发生变形。我们通过数值计算找出了大地运动的前倾角,结果表明,内部结构的存在放大了前倾角,反映了大地运动轨道内径向周期和轨道周期之间的差异。随着内部壳体数量的增加,前冲角单调增大,最终收敛到 N ⟶ ∞ 时的某个值。
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引用次数: 0
Impact of the magnetic horizon on the interpretation of the Pierre Auger Observatory spectrum and composition data 磁层对皮埃尔-奥格天文台光谱和成分数据解读的影响
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-30 DOI: 10.1088/1475-7516/2024/07/094
A. Abdul Halim, P. Abreu, M. Aglietta, I. Allekotte, K. Almeida Cheminant, A. Almela, R. Aloisio, J. Alvarez-Muñiz, J. Ammerman Yebra, G.A. Anastasi, L. Anchordoqui, B. Andrada, S. Andringa, L. Apollonio, C. Aramo, P.R. Araújo Ferreira, E. Arnone, J.C. Arteaga Velázquez, P. Assis, G. Avila, E. Avocone, A. Bakalova, F. Barbato, A. Bartz Mocellin, J.A. Bellido, C. Berat, M.E. Bertaina, G. Bhatta, M. Bianciotto, P.L. Biermann, V. Binet, K. Bismark, T. Bister, J. Biteau, J. Blazek, C. Bleve, J. Blümer, M. Boháčová, D. Boncioli, C. Bonifazi, L. Bonneau Arbeletche, N. Borodai, J. Brack, P.G. Brichetto Orchera, F.L. Briechle, A. Bueno, S. Buitink, M. Buscemi, M. Büsken, A. Bwembya, K.S. Caballero-Mora, S. Cabana-Freire, L. Caccianiga, F. Campuzano, R. Caruso, A. Castellina, F. Catalani, G. Cataldi, L. Cazon, M. Cerda, A. Cermenati, J.A. Chinellato, J. Chudoba, L. Chytka, R.W. Clay, A.C. Cobos Cerutti, R. Colalillo, M.R. Coluccia, R. Conceição, A. Condorelli, G. Consolati, M. Conte, ..
The flux of ultra-high energy cosmic rays reaching Earth above the ankle energy (5 EeV) can be described as a mixture of nuclei injected by extragalactic sources with very hard spectra and a low rigidity cutoff. Extragalactic magnetic fields existing between the Earth and the closest sources can affect the observed CR spectrum by reducing the flux of low-rigidity particles reaching Earth. We perform a combined fit of the spectrum and distributions of depth of shower maximum measured with the Pierre Auger Observatory including the effect of this magnetic horizon in the propagation of UHECRs in the intergalactic space. We find that, within a specific range of the various experimental and phenomenological systematics, the magnetic horizon effect can be relevant for turbulent magnetic field strengths in the local neighbourhood in which the closest sources lie of order Brms ≃ (50–100) nG (20 Mpc/ds)( 100 kpc/Lcoh)1/2, with ds the typical intersource separation and Lcoh the magnetic field coherence length. When this is the case, the inferred slope of the source spectrum becomes softer and can be closer to the expectations of diffusive shock acceleration, i.e., ∝ E-2. An additional cosmic-ray population with higher source density and softer spectra, presumably also extragalactic and dominating the cosmic-ray flux at EeV energies, is also required to reproduce the overall spectrum and composition results for all energies down to 0.6 EeV.
到达地球的超高能宇宙射线通量高于安克能量(5 EeV),可以描述为由银河系外源注入的核混合物,其光谱非常坚硬,截止刚度很低。存在于地球和最近来源之间的河外星系磁场会减少到达地球的低刚度粒子的通量,从而影响观测到的 CR 光谱。我们对频谱和皮埃尔-奥格天文台测量到的阵雨最大深度分布进行了综合拟合,其中包括这种磁水平线对 UHECR 在星系际空间传播的影响。我们发现,在各种实验和现象学系统性的特定范围内,磁水平线效应可能与本地邻域的湍流磁场强度有关,其中最近的源位于 Brms ≃ (50-100) nG (20 Mpc/ds)( 100 kpc/Lcoh)1/2,ds 是典型的源间距,Lcoh 是磁场相干长度。在这种情况下,推断出的源光谱斜率会变得更柔和,更接近扩散冲击加速度的预期,即∝E-2。要重现低至 0.6 EeV 的所有能量下的总体频谱和成分结果,还需要另外一个具有更高源密度和更柔和频谱的宇宙射线群,它可能也是银河系外的,并在 EeV 能量的宇宙射线通量中占主导地位。
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引用次数: 0
Quadratic perturbations of the Schwarzschild black hole: the algebraically special sector 施瓦兹柴尔德黑洞的二次扰动:代数特殊部门
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-30 DOI: 10.1088/1475-7516/2024/07/085
Jibril Ben Achour and Hugo Roussille
We investigate quadratic algebraically special perturbations (ASPs) of the Schwarzschild black hole. Their dynamics are derived from the expansion up to second order in perturbation of the most general algebraically special twisting vacuum solution of general relativity. Following this strategy, we present analytical expressions for the axial-axial, polar-polar and polar-axial source terms entering in the dynamical equations. We show that these complicated inhomogeneous equations can be solved analytically and we present explicit expressions for the profiles of the quadratic ASPs. As expected, they exhibit exponential growth both at the past and future horizons even in the non-linear regime. We further use this result to analyze the quadratic zero modes and their interpretation in terms of quadratic corrections to mass and spin of the Schwarzschild black hole. The present work provides a direct extension beyond the linear regime of the original work by Couch and Newman.
我们研究了施瓦兹柴尔德黑洞的二次代数特殊扰动(ASPs)。它们的动力学是从广义相对论最一般的代数特殊扭转真空解的扰动扩展到二阶推导出来的。根据这一策略,我们提出了进入动力学方程的轴-轴、极-极和极-轴源项的分析表达式。我们证明了这些复杂的非均质方程可以通过分析求解,并给出了四元 ASP 曲线的明确表达式。不出所料,即使在非线性状态下,它们在过去和未来的水平面上都呈现指数增长。我们进一步利用这一结果分析了二次零模及其对施瓦兹柴尔德黑洞质量和自旋二次修正的解释。目前的工作直接扩展了库奇和纽曼最初工作的线性范围。
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引用次数: 0
An implementation of nDGP gravity in Pinocchio 皮诺曹中 nDGP 重力的实现
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-30 DOI: 10.1088/1475-7516/2024/07/093
Yanling Song, Bin Hu, Cheng-Zong Ruan, Chiara Moretti and Pierluigi Monaco
In this paper we investigate dark matter structure formation in the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model using the PINOCCHIO algorithm. We first present 2nd order Lagrangian perturbation theory for the nDGP model, which shows that the 1st- and 2nd-order growth functions in nDGP are larger than those in ΛCDM. We then examine the dynamics of ellipsoidal collapse in nDGP, which is accelerated compared to ΛCDM due to enhanced gravitational interactions. Running the nDGP-PINOCCHIO code with a box size of 512 Mpc h-1 and 10243 particles, we analyze the statistical properties of the output halo catalogs, including the halo power spectrum and halo mass function. The calibrated PINOCCHIO halo power spectrum agrees with N-body simulations within 5% in the comoving wavenumber range k<0.3 (h Mpc-1) at redshift z=0. The agreement is extended to smaller scales for higher redshifts. For the cumulative halo mass function, the agreement between N-body and PINOCCHIO is also within the simulation scatter.
本文利用 PINOCCHIO 算法研究了 Dvali-Gabadze-Porrati (nDGP)模型正常分支中暗物质结构的形成。我们首先提出了 nDGP 模型的二阶拉格朗日扰动理论,结果表明 nDGP 中的一阶和二阶增长函数比ΛCDM 中的要大。然后,我们研究了 nDGP 中的椭球坍缩动力学,由于引力相互作用的增强,nDGP 中的椭球坍缩比 ΛCDM 中的椭球坍缩加速。我们以 512 Mpc h-1 的盒大小和 10243 个粒子运行 nDGP-PINOCCHIO 代码,分析了输出光环星表的统计特性,包括光环功率谱和光环质量函数。校准后的 PINOCCHIO 光环功率谱与 N-体模拟的吻合度在 5%以内,即在红移 z=0 时,在移动波数范围 k<0.3 (h Mpc-1)。在累积光环质量函数方面,N-body 和 PINOCCHIO 的一致性也在模拟散度范围之内。
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引用次数: 0
Generalised conditions for rapid-turn inflation 快速转折通货膨胀的一般条件
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-29 DOI: 10.1088/1475-7516/2024/07/079
Raúl Wolters, Oksana Iarygina and Ana Achúcarro
Rapid-turn slow-roll inflationary trajectories have been shown to be an attractor in two-field models, provided the turn rate is near constant and larger than the slow-roll parameters. These trajectories can produce primordial spectra consistent with current observations on CMB scales. We present the generalized consistency condition for sustained rapid-turn inflationary trajectory with two fields, arbitrary field-space metric and potential valid for any value of the turn rate. This has to be supplemented by a second condition to ensure slow roll evolution. Both conditions together constitute a tool to identify inflationary trajectories with arbitrary values of the turning rate without having to solve the equations of motion. We present a Python package for the numerical identification of regions in field-space and parameter space that allow for rapid-turn trajectories.
快速转动的慢速膨胀轨迹已被证明是双场模型的吸引子,条件是转动率接近恒定且大于慢速转动参数。这些轨迹可以产生与当前 CMB 尺度观测结果一致的原始光谱。我们提出了具有两个场、任意场空间度量和对任何转折率值都有效的势的持续快速转折膨胀轨迹的广义一致性条件。这必须辅以第二个条件,以确保缓慢的翻滚演化。这两个条件共同构成了一个工具,无需求解运动方程即可识别具有任意转向率值的膨胀轨迹。我们介绍了一个 Python 软件包,用于对场空间和参数空间中允许快速翻转轨迹的区域进行数值识别。
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引用次数: 0
The hierarchical cosmic web and assembly bias 分层宇宙网和组装偏差
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-29 DOI: 10.1088/1475-7516/2024/07/083
J.M. Coloma-Nadal, F.-S. Kitaura, J.E. García-Farieta, F. Sinigaglia, G. Favole and D. Forero Sánchez
Accurate modeling of galaxy distributions is paramount for cosmological analysis using galaxy redshift surveys. However, this endeavor is often hindered by the computational complexity of resolving the dark matter halos that host these galaxies. To address this challenge, we propose the development of effective assembly bias models down to small scales, i.e., going beyond the local density dependence capturing non-local cosmic evolution. We introduce a hierarchical cosmic web classification that indirectly captures up to third-order long- and short-range non-local bias terms. This classification system also enables us to maintain positive definite parametric bias expansions. Specifically, we subdivide the traditional cosmic web classification, which is based on the eigenvalues of the tidal field tensor, with an additional classification based on the Hessian matrix of the negative density contrast. We obtain the large-scale dark matter field on a mesh with ~3.9 h-1 Mpc cell side resolution through Augmented Lagrangian Perturbation Theory. To assess the effectiveness of our model, we conduct tests using a reference halo catalogue extracted from the UNIT project simulation, which was run within a cubical volume of 1 h-1 Gpc side. The resulting mock halo catalogs, generated through our approach, exhibit a high level of accuracy in terms of the one-, two- and three-point statistics. They reproduce the reference power-spectrum within better than 2 percent accuracy up to wavenumbers k ~ 0.8 h Mpc-1 and provide accurate bispectra within the scales that are crucial for cosmological analysis. This effective bias approach provides a forward model appropriate for field-level cosmological inference and holds significant potential for facilitating cosmological analysis of galaxy redshift surveys, particularly in the context of projects such as DESI, EUCLID, and LSST.
星系分布的精确建模对于利用星系红移测量进行宇宙学分析至关重要。然而,由于解析星系所在的暗物质晕的计算复杂性,这项工作常常受到阻碍。为了应对这一挑战,我们提出建立有效的组装偏差模型,并将其细化到小尺度,即超越局部密度依赖,捕捉非局部宇宙演化。我们引入了一种分级宇宙网分类法,它可以间接捕捉高达三阶的长程和短程非局部偏倚项。这一分类系统还使我们能够保持正定参数偏差扩展。具体来说,我们将基于潮汐场张量特征值的传统宇宙网分类细分为基于负密度对比的赫西安矩阵的附加分类。我们通过增强拉格朗日扰动理论(Augmented Lagrangian Perturbation Theory),在约 3.9 h-1 Mpc 单元边分辨率的网格上获得了大尺度暗物质场。为了评估我们模型的有效性,我们使用从 UNIT 项目模拟中提取的参考光环目录进行了测试,该模拟是在 1 h-1 Gpc 边长的立方体体积内运行的。通过我们的方法生成的模拟光环目录在单点、两点和三点统计方面都表现出很高的精确度。在波数 k ~ 0.8 h Mpc-1 的范围内,它们重现参考功率谱的精确度优于 2%,并在对宇宙学分析至关重要的尺度内提供了精确的双谱。这种有效偏差方法提供了一种适合于场级宇宙学推断的前向模型,在促进星系红移测量的宇宙学分析方面具有巨大潜力,特别是在DESI、EUCLID和LSST等项目中。
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引用次数: 0
The anomaly of the CMB power with the latest Planck data 最新普朗克数据显示的 CMB 功率异常
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-29 DOI: 10.1088/1475-7516/2024/07/080
M. Billi, R.B. Barreiro and E. Martínez-González
The lack of power anomaly is an unexpected feature observed at large angular scales in the maps of Cosmic Microwave Background (CMB) produced by the COBE, WMAP and Planck satellites. This signature, which consists in a missing of power with respect to that predicted by the ΛCDM model, might hint at a new cosmological phase before the standard inflationary era. The main point of this paper is taking into account the latest Planck polarisation data to investigate how the CMB polarisation improves the understanding of this feature. With this aim, we apply to the latest Planck data, both PR3 (2018) and PR4 (2020) releases, a new class of estimators capable of evaluating this anomaly by considering temperature and polarisation data both separately and in a jointly way. This is the first time that the PR4 dataset has been used to study this anomaly. To critically evaluate this feature, taking into account the residuals of known systematic effects present in the Planck datasets, we analyse the cleaned CMB maps using different combinations of sky masks, harmonic range and binning on the CMB multipoles. Our analysis shows that the estimator based only on temperature data confirms the presence of a lack of power with a lower-tail-probability (LTP), depending on the component separation method, ≤ 0.33% and ≤ 1.76% for PR3 and PR4, respectively. To our knowledge, the LTP≤ 0.33% for the PR3 dataset is the lowest one present in the literature obtained from Planck 2018 data, considering the Planck confidence mask. We find significant differences between these two datasets when polarisation is taken into account most likely due to a different level of systematics. Especially, the analysis with PR3 data, unlike that with PR4, seems to point towards a lack of power at large scales also for polarisation. Moreover, we also show that for the PR3 dataset the inclusion of the subdominant polarisation information provides estimates that are less likely accepted in a ΛCDM cosmological model than the only-temperature analysis over the entire harmonic-range considered. In particular, at ℓmax = 26, we found that no simulation has a value as low as the data for all the pipelines.
在 COBE、WMAP 和普朗克卫星绘制的宇宙微波背景(CMB)图中,在大角度尺度上观测到了一个意想不到的特征,即缺乏功率异常。这一特征包括相对于ΛCDM模型预测的功率缺失,可能暗示了标准暴胀时代之前的一个新的宇宙学阶段。本文的重点是考虑最新的普朗克极化数据,研究 CMB 极化如何改善对这一特征的理解。为此,我们将最新的普朗克数据(PR3(2018)和PR4(2020)版本)应用于一类新的估算器,该估算器能够通过单独和联合考虑温度和极化数据来评估这一异常。这是 PR4 数据集首次用于研究这一异常现象。考虑到普朗克数据集中已知系统效应的残差,我们使用不同的天空掩码、谐波范围和 CMB 多极子分档组合,对清理后的 CMB 地图进行了分析。我们的分析表明,仅基于温度数据的估计值证实了功率不足的存在,根据分量分离方法的不同,PR3 和 PR4 的低尾概率(LTP)分别≤ 0.33%和≤ 1.76%。据我们所知,考虑到普朗克置信掩模,PR3 数据集的 LTP≤0.33% 是目前文献中从普朗克 2018 数据中获得的最低值。我们发现,在考虑极化因素时,这两个数据集之间存在明显差异,这很可能是由于系统学水平不同造成的。特别是,与 PR4 数据不同,PR3 数据的分析似乎表明在大尺度上缺乏偏振的能力。此外,我们还表明,对于 PR3 数据集来说,在考虑的整个谐波范围内,纳入次主极化信息所提供的估计值,与只进行温度分析相比,不太可能被ΛCDM 宇宙学模型所接受。特别是在ℓmax = 26时,我们发现所有管道的模拟值都没有数据那么低。
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引用次数: 0
A diffused background from axion-like particles in the microwave sky 微波天空中类似轴子粒子的扩散背景
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-29 DOI: 10.1088/1475-7516/2024/07/084
Harsh Mehta and Suvodip Mukherjee
The nature of dark matter is an unsolved cosmological problem and axions are one of the weakly interacting cold dark matter candidates. Axions or ALPs (Axion-like particles) are pseudo-scalar bosons predicted by beyond-standard model theories. The weak coupling of ALPs with photons leads to the conversion of CMB photons to ALPs in the presence of a transverse magnetic field. If they have the same mass as the effective mass of a photon in a plasma, the resonant conversion would cause a polarized spectral distortion leading to temperature fluctuations with the distortion spectrum. The probability of resonant conversion depends on the properties of the cluster such as the magnetic field, electron density, and its redshift. We show that this kind of conversion can happen in numerous unresolved galaxy clusters up to high redshifts, which will lead to a diffused polarised anisotropy signal in the microwave sky. The spectrum of the signal and its shape in the angular scale will be different from the lensed CMB polarization signal. This new polarised distortion spectrum will be correlated with the distribution of clusters in the universe and hence, with the large-scale structure. The spectrum can then be probed using its spectral and spatial variation with respect to the CMB and various foregrounds. An SNR of ~ 4.36 and ~ 93.87 are possible in the CMB-S4 145 GHz band and CMB-HD 150 GHz band respectively for a photon-ALPs coupling strength ofgaγ= 10-12GeV-1using galaxy clusters beyond redshiftz= 1. The same signal would lead to additional RMS fluctuations of ~7.5 × 10-2μK at 145 GHz. In the absence of any signal, future CMB experiments such as Simons Observatory (SO), CMB-S4, and CMB-HD can put constraints on the coupling strength better than current bounds from particle physics experiment CERN Axion Solar Telescope (CAST).
暗物质的性质是一个悬而未决的宇宙学问题,而轴子是弱相互作用冷暗物质候选物质之一。轴子或ALPs(类轴子粒子)是超标准模型理论所预言的伪标量玻色子。ALPs与光子的弱耦合导致CMB光子在横向磁场的作用下转化为ALPs。如果它们的质量与等离子体中光子的有效质量相同,共振转换将导致极化光谱畸变,从而导致温度随畸变光谱波动。共振转换的概率取决于星团的特性,如磁场、电子密度和红移。我们的研究表明,这种转换可以发生在许多未解析的星系团中,直至高红移,这将导致微波天空中出现弥散的极化各向异性信号。该信号的频谱及其角尺度形状将不同于透镜CMB极化信号。这种新的偏振扭曲频谱将与宇宙中的星团分布相关,从而与大尺度结构相关。然后就可以利用它相对于 CMB 和各种前景的光谱和空间变化来探测这个频谱。当光子-ALPs 耦合强度为gaγ= 10-12GeV-1 时,利用红移兹= 1 以外的星系团,在 CMB-S4 145 GHz 波段和 CMB-HD 150 GHz 波段的信噪比可能分别为 ~4.36 和 ~93.87。在 145 GHz 波段,同样的信号会导致约 7.5 × 10-2μK 的额外均方根波动。在没有任何信号的情况下,未来的CMB实验,如西蒙斯天文台(Simons Observatory,SO)、CMB-S4和CMB-HD,可以对耦合强度施加比目前来自粒子物理实验欧洲核子研究中心轴心太阳望远镜(CERN Axion Solar Telescope,CAST)的约束更好的约束。
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引用次数: 0
Reparametrization invariant action for gravity with dynamical determinant of metric 具有度量动态行列式的重定性不变引力作用
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-29 DOI: 10.1088/1475-7516/2024/07/082
J. Klusoň
We present manifestly reparametrization invariant action for theory of gravity with dynamical determinant of metric. We show that it is similar to a reparametrization invariant action for unimodular gravity. We determine canonical form of the action and study structure of constraints.
我们提出了具有度量动态行列式的引力理论的明显重参数不变作用。我们证明它类似于单模态引力的重参数不变作用。我们确定了作用的典型形式,并研究了约束的结构。
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引用次数: 0
Spinning Proca-Higgs balls, stars and hairy black holes 旋转的普罗卡-希格斯球、恒星和毛茸茸的黑洞
IF 6.4 2区 物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS Pub Date : 2024-07-29 DOI: 10.1088/1475-7516/2024/07/081
Carlos Herdeiro, Eugen Radu and Etevaldo dos Santos Costa Filho
Recently, spherical and static flat space solitons (balls) and self-gravitating, everywhere regular, asymptotically flat solitons (stars) were constructed in an Einstein-Proca-Higgs model [1], where a complex vector field gains mass by coupling to a real scalar field with a Higgs-type potential. The Proca-Higgs model serves as a UV completion of a complex Proca model with self-interactions. Here, we construct and examine the mathematical and physical properties of rotating configurations. In particular, rotation allows horizon-bearing solutions, including stationary clouds surrounding Kerr black holes and their non-linear continuation into black holes with Proca-Higgs hair.
最近,在爱因斯坦-普罗卡-希格斯模型[1]中构建了球形和静态扁平空间孤子(球)以及自引力、无处不在的规则渐近扁平孤子(星),其中复矢量场通过与具有希格斯型势能的实标量场耦合而获得质量。普罗卡-希格斯模型是具有自相互作用的复杂普罗卡模型的紫外补全。在这里,我们构建并研究了旋转构型的数学和物理特性。特别是,旋转允许有地平线的解,包括围绕克尔黑洞的静止云及其与普罗卡-希格斯发黑洞的非线性延续。
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引用次数: 0
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Journal of Cosmology and Astroparticle Physics
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