Giuseppe Alberti
We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition $<γ> \geq 4/3$ of the isotropic regime. Also, we discuss some applications of the criterion.
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Stability and instability results for equilibria of a (relativistic) self-gravitating collisionless gas -- A review
本文为综述类研究，聚焦广义相对论下Einstein-Vlasov系统稳态的稳定性与不稳定性，同时结合Vlasov-Poisson系统及相对论性Vlasov-Poisson系统展开对比讨论，梳理自引力无碰撞气体平衡态的相关研究结果。
We show that a generic relativistic membrane with in-plane pressure and surface density having the same sign is unstable with respect to a series of warping mode instabilities with high wave numbers. We also examine the criteria of instability for commonly studied exotic compact objects with membranes, such as gravastars, AdS bubbles and thin-shell wormholes. For example, a gravastar which satisfies the weak energy condition turns out to be dynamically unstable. A thin-layer black hole mimicker is stable only if it has positive pressure and negative surface density (such as a wormhole), or vic…
Instability of Gravitating Sphalerons
通过研究一类径向微扰的频谱，证明了具有Higgs偶联体的$SU(2)$ Einstein-Yang-Mills-Higgs系统引力正则散射子解的不稳定性.借助于变分原理，我们证明了总是存在不稳定模式。我们的方法的优点是，不需要详细的知识的平衡解决方案。然而，它并不直接适用于黑洞。
Beyond Classical Instability Limits of Anisotropic Self-gravitating Fluid Configurations in Hu-Sawicki Inspired f(R) Gravity
在 Hu-Sawicki f(R) 引力模型中，研究非静态轴对称自引力流体的动力学不稳定性，通过线性扰动导出坍缩方程，发现不稳定性条件依赖于绝热指数、能量密度、各向异性压力、度规扰动及高阶曲率修正。
Dynamical evolution of unstable self-gravitating scalar solitons
最近，人们发现了全局正则自引力标量孤子的静态和球对称结构，这些结构对于径向线性扰动是不稳定的。在本文中，我们研究了这种配置的动力学演化，并表明，根据初始扰动的符号，孤子要么崩溃到史瓦西黑洞，否则"爆炸“成一个向外移动的域壁。
Self-adjoint wave equations for dynamical perturbations of self-gravitating fields
它表明，在静态时空的线性扰动的动力学演化是由一个约束的波动方程的外在曲率张量。波算子的空间部分是明显的椭圆和自伴的。与度量公式相反，引力微扰理论的曲率基方法以自然的方式推广到自引力物质场。本文还演示了如何得到自引力非阿贝尔规范场、希格斯场和理想流体的对称脉动方程。对于真空时空中的真空涨落，重新导出了Regge-Wheeler方程和Zerilli方程。
In this paper, we have continued the work of Herrera \emph{et al.} \cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a spherically symmetric fluid exhibiting locally anisotropic pressure along with the energy density, is taken under consideration. The perturbation scheme is imposed on modified field equations and the dynamical equations. The collapse equation is devised from these perturbed equations which stimulates to disclose the instability zone under both Newtonian and post-Newtonian constraints. It is wrapped up by concluding that dynamical instability is inte…
This paper is devoted to analyze the dynamical instability of a self-gravitating object undergoes to collapse process. We take the framework of generalized teleparallel gravity with cylindrically symmetric gravitating object. The matter distribution is represented by locally anisotropic energy-momentum tensor. We develop basic equations such as dynamical equations along with matching conditions and Harrison-Wheeler equation of state. By applying linear perturbation strategy, we construct collapse equation which is used to accomplish the instability ranges in Newtonian and post-Newtonian regime…
The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein-Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfec…
We investigate the existence and the stability of spherically symmetric thermal equilibrium states of the self-gravitating many-particle system which satisfies the Einstein-Vlasov equations with a negative cosmological constant. While a thermal equilibrium state of the self-gravitating particle system cannot have a finite mass without an artificial wall in the asymptotically flat case, in the asymptotically AdS case, the total mass can be finite without any artificial wall due to the AdS potential barrier. In this case, the typical size of the system is characterized by the AdS radius. The equ…
The dynamical stability of massive thin shells with a given equation of state (EOS) is here compared (both for the barotropic and non-barotropic case) with the results coming from thermodynamical stability. Our results show that the restrictions in the parameter space of equilibrium configurations of the shell following from thermodynamical stability are much more stringent that those obtained from dynamical stability. As a byproduct, we furnish evidence that the link between the maximum mass along a sequence of equilibrium configurations and the onset of dynamical stability is valid for EOS o…
Collisionless self-gravitating systems in f(R)-gravity within Palatini approach and relativistic Boltzmann equation in the Newtonian approach
本文在弱场近似下分析了f（R）-引力和Boltzmann方程描述的无碰撞自引力系统的动力学，重点研究了这些系统的Jeans不稳定性。这种近似下的场方程是在Palatini形式主义中得到的。通过对耦合方程的求解，得到了由色散关系给出的无限大均匀流体-恒星系统的坍缩判据。将这个结果与标准情形和度量形式中f（R）-引力情形的结果进行了比较，以了解它们之间的差异。不稳定性的极限因采用哪种引力理论而异。
Energy and angular momentum in strong gravitating systems
引入了一个准定域框架，将孤立视界和动力学俘获视界的能量和角动量概念推广到一般的强引力系统.
Stability of a Class of Non-Static Axial Self-Gravitating Systems in $f(R)$ Gravity
本文分析了一类非静态限制性轴对称各向异性物质分布时空的稳定域。我们考虑$f(R)=R+εR^2$模型，假设轴向自引力系统在大的过去时间内处于流体静力平衡。考虑到流体静力相的扰动，我们建立了动力学和坍缩方程，并探讨了牛顿和后牛顿体系的动力学不稳定性。借助刚度参数$Γ_1$，得出了$f(R)$模型的压力各向异性、能量密度和高曲率项等物理参数的径向分布影响不稳定范围的结论。
Nonlinear instability and solitons in a self-gravitating fluid
本文研究球形自引力流体模型，通过多尺度展开方法推导出控制扰动包络的球形非线性 Schrödinger 方程，预测了可产生球形孤子态的调制不稳定性，并指出孤子轮廓可用于描述星系边缘暗物质晕的形状。
The present work deals with the dynamics of radiating star which is considered to be expansion free cylindrical symmetric dust dissipative fluids. Several treatments are adopted for the description of geometrical and physical features of such stars. Firstly, it is shown that, the dynamical star does not permit the streaming out limit and diffusion approximation and also proved that acceleration and dissipation are necessary for its dynamical evolution. It has also shown that, a static expansion free cylinder must be non-radiating. Secondly, the existence of cavity model and self-similar soluti…
Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: Dynamical equivalence and consequences
受活动星系核中心区域质量观测测定方法的启发，我们研究了在引力理想流体源内部，测地运动和广义相对论流体动力学流相互动力学等价的条件。动力学等价依赖于相应的（协变表示）运动微分方程之间的功能相似性，并通过保角变换获得。在这种情况下，这两种运动的解的空间是同构的。换句话说，给定“理想流体中的流体动力学流动”问题的解，人们总是可以构造形式上等价于“流体元素的测地线运动”问题的解，反之亦然。因此，我们表明，观测确定的活动星系核的核质量是高估相对于真实的，物理的。我们评估了相应的质量过剩，并表明它并不总是可以忽略不计的相对于中央暗物体的质量，而在某些情况下，甚至可以大于所涉及的环核气体的静止质量。
Multimessenger Signatures of Tilted, Self-Gravitating, Black Hole Disks
研究倾斜自引力黑洞盘的非轴对称不稳定性，揭示磁流体动力学模拟中引力波发射与喷流机制，支持其作为多信使源的角色。
On free evolution of self gravitating, spherically symmetric waves
本文对满足波动方程的自引力球对称标量场进行了数值自由演化。演化方程可以写成非常简单的形式，并且在Eddington-Finkelstein坐标系中是对称双曲的。该系统的简单性允许显示和处理这些坐标中存在的典型规范不稳定性。数值演化是用标准的四阶空间和时间线方法进行的。时间算法是龙格-库塔，而空间离散导数是对称的（非耗散的）。的约束条件下保存的演变（数值误差内），我们能够重现几个已知的结果。
Gravothermal Catastrophe and Generalized Entropy of Self-Gravitating Systems
我们提出了Tsallis的广义熵的自引力系统的热力学的第一个物理应用。被限制在半径为$r_e$的球形空腔中的恒星系统表现出一种不稳定性，即所谓的重力热灾变，最初是由Antonov（1962）和Lynden-Bell & Wood（1968）根据相空间分布函数的最大熵原理研究的。与以往的分析使用玻尔兹曼-吉布斯熵，我们应用Tsallis型广义熵寻求平衡的标准。这样，Vlassov-Poisson系统的分布函数就可以化为恒星多变系统的分布函数。通过计算Tsallis熵的二阶变分和求解零本征值问题，我们发现在多变性指数$n>5$的情况下出现了重力热不稳定性.得到了表征失稳开始的临界点，这与标准转折点分析的结果完全吻合。结果表明，Tsallis熵对自引力系统的长程性质确实是适用和可行的。
Solar system observations have traditionally allowed for very stringent tests of Einstein's theory of general relativity. We here revisit the possibility of using these observations to constrain gravitational parity violation as encapsulated in dynamical Chern-Simons gravity. Working in the small-coupling and post-Newtonian approximations, we calculate analytically the scalar field and the gravitomagnetic sector of the gravitational field in the interior and the exterior of an isolated, weakly-gravitating object with uniform rotation and a quadrupolar mass deformation. We find that the asympto…
We study the Jeans gravitational instability for a mixture of baryonic and dark matter particles, in the post-Newtonian approximation. We adopt a kinetic model consisting of a coupled system of post-Newtonian collisionless Boltzmann equations, for each species, coupled to the post-Newtonian Poisson equations. We derive the stability criterion, accounting for both post-Newtonian corrections and the presence of dark matter. It is shown that both effects give rise to smaller Jeans masses, in comparison with the standard Jeans criterion, meaning that a smaller mass is needed to begin the gravitati…
Bifurcation and fine structure phenomena in critical collapse of a self-gravitating $σ$-field
在前人对自引力SU（2）$σ$场引力坍缩临界行为研究的基础上，利用高精度数值方法，我们揭示了隐藏在参数空间狭窄窗口中的精细结构.我们认为，这个数值发现有一个自然的解释临界崩溃的动力系统框架内。
Self-gravitating splitting thin shells
在本文中，我们表明，薄壳在球对称时空，其内容描述了一对非相互作用的球对称物质场，一般表现出不稳定性对无穷小分离的组成领域。我们给出明确的例子和构造的解决方案，代表一个壳分裂成两个壳。然后，我们将这些结果推广到5维Schwarzschild-AdS体时空，这是一个典型的情况下，膜世界模型，并表明，同样的稳定性分析和分裂解决方案可以构建。我们发现，一个广泛提出的膜世界模型家族在这个意义上是非常不稳定的。最后，我们讨论可能的解释，这些功能和它们的关系集中源的初始值问题。
Stability properties of black holes in self-gravitating nonlinear electrodynamics
我们分析了自引力非线性电动力学中黑洞解相对于度规和电磁场的任意线性涨落的动力学稳定性。特别是，我们推导出简单的电磁拉格朗日条件，这意味着线性稳定域的外部通信。我们表明，这些条件下举行的定期黑洞解发现的Ayon-Beato和加西亚。
We review the history of the self-gravitating Fermi gas in Newtonian gravity and general relativity. We mention applications to white dwarfs, neutron stars and dark matter halos. We describe the nature of instabilities and phase transitions in the self-gravitating Fermi gas as energy (microcanonical ensemble) or temperature (canonical ensemble) is reduced. When $N<N_{\rm OV}$, where $N_{\rm OV}$ is the Oppenheimer-Volkoff critical particle number, the self-gravitating Fermi gas experiences a gravothermal catastrophe at $E_c$ stopped by quantum mechanics (Pauli's exclusion principle). The equil…
In this article, we have studied a cylindrically symmetric self-gravitating dynamical object via complexity factor which is obtained through orthogonal splitting of Reimann tensor in $f(R,T)$ theory of gravity. Our study is based on the definition of complexity for dynamical sources, proposed by Herrera \cite{12b}. We actually want to analyze the behavior of complexity factor for cylindrically symmetric dynamical source in modified theory. For this, we define the scalar functions through orthogonal splitting of Reimann tensor in $f(R,T)$ gravity and work out structure scalars for cylindrical g…
We determine the caloric curves of classical self-gravitating systems at statistical equilibrium in general relativity. In the classical limit, the caloric curves of a self-gravitating gas depend on a unique parameter $ν=GNm/Rc^2$, called the compactness parameter, where $N$ is the particle number and $R$ the system's size. Typically, the caloric curves have the form of a double spiral. The "cold spiral", corresponding to weakly relativistic configurations, is a generalization of the caloric curve of nonrelativistic classical self-gravitating systems. The "hot spiral'", corresponding to strong…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e., relativistic models of stars. Such steady states are embedded into one-parameter families parameterized by their central redshift $κ>0$. We prove their linear instability when $κ$ is sufficiently large, i.e., when they are strongly relativistic, and that the instability is driven by a growing mode. Our work confirms the scenario of dynamic instability propo…
Detecting Collective Excitations in Self-Gravitating Bose-Einstein Condensates via Faraday Waves
该研究提出以法拉第波为探针探测自引力玻色-爱因斯坦凝聚体的集体激发，通过半经典方法推导阻尼Mathieu方程分析两类不稳定性特征，结合数值模拟验证理论框架并提供实验指导。
Dynamical N-body Equlibrium in Circular Dilaton Gravity
我们得到了一维相对论性自引力系统N体问题的一个新的精确平衡解。它对应于一个有N个物体的圆的时空的膨胀/收缩，这些物体在圆周围彼此具有相等的适当距离。我们的方法是直截了当地推广到其他粒子引力理论，并提供了一类新的解决方案，以进一步研究（相对论）一维自引力系统。
Self-gravitating stationary spherically symmetric systems in relativistic galactic dynamics
本文研究了相对论性星系动力学中的平衡态，这些平衡态是由无碰撞物质的Einstein-Vlasov系统的解所描述的。我们重铸的方程到一个定期的三维系统的自治一阶常微分方程的有界状态空间。基于动力系统分析，我们推导出新的定理，保证稳态解具有有限的半径和质量。
We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born-Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell- Boltzmann distribution function $f_0(v)$. Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale le…
Self-gravitating Stellar Systems and Non-extensive Thermostatistics
在介绍了自引力系统的基本性质之后，我们给出了Tsallis广义熵在分析自引力系统热力学性质中的应用。通过极值的Tsallis熵，我们得到一个状态方程称为恒星多面体。对于一个被完全反射壁所限制的自引力恒星系统，我们讨论了它的负比热引起的热力学不稳定性。极值作为一个准平衡的作用也证明了从N体模拟的结果。
Instability of Flat Space Enclosed in a Cavity
本文考虑封闭在具有完全反射壁的类时世界管$R\times S^3$中的球对称自引力无质量标量场。数值证据表明，任意小的通用初始数据演化成一个黑洞。
Quasi-stationary solutions of self-gravitating scalar fields around black holes
最近的微扰研究表明，在黑洞周围存在长寿命的准定态标量场。特别是，这样的配置已被发现生存的宇宙学时间尺度，这是一个可行的暗物质晕模型的基础上，这种类型的结构的星系的要求。本文对被自引力标量场包围的动态非旋转黑洞进行了一系列的相对论数值模拟。在球坐标系下，在球对称假设下，数值求解了由爱因斯坦方程和克莱因-戈登方程组成的耦合方程组。我们的结果证实了在具有丰富标量场环境的高动态时空中，非旋转黑洞周围存在振荡的、长寿命的、自引力的标量场组态。我们的数值模拟是长期稳定的，并允许提取的谐振频率，使线性化制度中获得的结果进行直接比较。我们模拟的一个副产品是爱因斯坦方程的合理长寿命解中存在简并性，这将引起测试粒子的相同运动，无论是否存在准束缚态。
Critical Dimension for Stable Self-gravitating Stars in AdS
我们在AdS空间中用线性状态方程$P=a ρ$研究了自引力星，其中$a$是一个常数参数.存在一个临界尺寸，超过这个尺寸，恒星在任何中心能量密度下都是稳定的;低于这个尺寸，对于某个中心能量密度，存在一个最大质量配置，当中心能量密度继续增加时，配置变得不稳定。我们发现临界维数依赖于参数$a$，当$a$从$a=0$变为1时，临界维数从$d=11.1429$变为10.1291。对于任何$a \in [0,1]$，动力学稳定的自引力位形的最低整数维数应该是$d=12$，而不是$d=11$，后者是AdS空间中自引力辐射位形的情况。
Self-gravitating isothermal sphere in an expanding background
本研究在膨胀宇宙背景下建立自引力等温球的自洽引力热力学，发现正则与巨正则系综中平衡态均存在不稳定性，并指出高红移下该不稳定性可形成特定质量与半径的重子气体云。
We develop a general formalism to determine the statistical equilibrium states of self-gravitating systems in general relativity and complete previous works on the subject. Our results are valid for an arbitrary form of entropy but, for illustration, we explicitly consider the Fermi-Dirac entropy for fermions. The maximization of entropy at fixed mass-energy and particle number determines the distribution function of the system and its equation of state. It also implies the Tolman-Oppenheimer-Volkoff equations of hydrostatic equilibrium and the Tolman-Klein relations. Our paper provides all th…
The generalization of the Regge-Wheeler equation for self-gravitating matter fields
它表明，在一个静态的时空扰动的动力学演化是由一个标准的脉动方程的外在曲率张量。脉动方程的核心是一个波动算子，其空间部分显然是自伴的。与度量公式相反，引力微扰理论的曲率基方法以自然的方式推广到自引力物质场。对于某个相关的扰动子空间的脉动算子是对称的关于一个积极的内积，因此允许谱理论被应用。特别是，这是球对称背景配置的奇宇称扰动的情况。作为一个例子，自引力，非阿贝尔规范场的脉动方程被明确地证明是对称的引力，杨米尔斯，和非对角扇区。
Gravothermal Catastrophe and Tsallis' Generalized Entropy of Self-Gravitating Systems III. quasi-equilibrium structure using normalized q-values
本文重新讨论了由Tsallis的非广延熵引起的恒星自引力系统的热力学性质问题。以前的论文（Taruya & Sakagami，Physica A 307（2002）185（cond-mat/0107494）; ibid.（2002）in press（cond-mat/0204315））已经揭示了以所谓的恒星多变性为特征的Tsallis熵的极值状态具有一致的热力学结构，其预测了由于负比热引起的热力学不稳定性。然而，他们的分析严重依赖于使用标准线性平均值的旧Tsallis形式主义。本文在前人研究的基础上，利用规范化的q-期望值研究了基于标准框架的均衡结构。然后证明，Tsallis熵的新极值状态基本上与先前的结果保持不变，即，恒星准平衡分布可用恒星多面体描述。虽然绝热壁中限制的系统的热力学稳定性完全同意与以前的研究，从而稳定/不稳定的标准保持不变，稳定性分析揭示了一个新的平衡性质的热浴包围的系统。在任何情况下，稳定性/不稳定性的标准是一致的解释，从存在的负比热和形式主义内，恒星多变的特点是作为一个合理的非广泛的Meta平衡态。
The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the structure of the fluid distribution, but also the condition of minimal complexity of the pattern of evolution. As we shall see these two issues are deeply intertwined. For the complexity factor of the structure we choose the same as for the static case, whereas for the simplest pattern of evolution we assume the homologous condition. The dissipative and non-dis…
We present new regular solutions of Einstein-charged scalar field theory in a cavity. The system is enclosed inside a reflecting mirror-like boundary, on which the scalar field vanishes. The mirror is placed at the zero of the scalar field closest to the origin, and inside this boundary our solutions are regular. We study the stability of these solitons under linear, spherically symmetric perturbations of the metric, scalar and electromagnetic fields. If the radius of the mirror is sufficiently large, we present numerical evidence for the stability of the solitons. For small mirror radius, som…
Self-gravitating kink solutions of a two-dimensional dilaton gravity are revisited in this work. Analytical kink solutions are derived from a concise superpotential formalism of the dynamical equations. A general analysis on the linear stability is conducted for an arbitrary static solution of the model. After gauge fixing, a Schrödinger-like equation with factorizable Hamiltonian operator is obtained, which ensures the linear stability of the solution.
The gravitational instability, responsible for the formation of the structure of the Universe, occurs below energy thresholds and above spatial scales of a self-gravitating expanding region, when thermal energy can no longer counterbalance self-gravity. I argue that at sufficiently-large scales, dark energy may restore thermal stability. This stability re-entrance of an isothermal sphere defines a turnaround radius, which dictates the maximum allowed size of any structure generated by gravitational instability. On the opposite limit of high energies and small scales, I will show that an ideal,…
Equilibrium configurations of fluids and their stability in higher dimensions
我们研究平衡的形状，稳定性和可能的分歧图的流体在更高的维度，一起举行的表面张力或自引力。我们考虑了自引力椭球的平衡形状和稳定性问题，建立了将MacLaurin序列推广到高维的形式。我们表明，这种简单的模型，对自己的利益，也提供了准确的描述，他们的广义相对论亲属与事件视界。这里给出的例子暗示了一些与模型无关的动力学，因此也暗示了一些普遍性：光滑的物体似乎总是可以用两种“复制”（自引力或表面张力）来很好地描述。作为一个例子，我们表现出一个不稳定的困扰自引力（牛顿）流体圆柱。这种不稳定性在牛顿引力中与广义相对论中的格雷戈里-拉弗拉姆不稳定性完全相似。另一个例子考虑的是一个自引力牛顿环面的均匀不可压缩流体。我们在广义相对论中恢复了黑环的特征。
We study the global stability of a self-gravitating disk in the context of Modified Gravity (MOG) using N-body simulations. This theory is a relativistic scalar-tensor-vector theory of gravity and presented to address the dark matter problem. In the weak field limit MOG possesses two free parameters $α$ and $μ_0$ which have been already determined using rotation curve data of spiral galaxies. The evolution of a stellar self-gravitating disk and more specifically the bar instability in MOG is investigated and compared to a Newtonian case. Our models have exponential and Mestel-like surface dens…
Soliton solution of a gravitating chiral quark soliton model: dynamical fermion and Dirac-sea in general relativity
本文在球对称弯曲时空中将手征夸克孤子模型与爱因斯坦引力自洽求解，发现狄拉克海稀释引力效应，并在大动力学质量下导致负ADM质量。
Caustics in Self-gravitating N-body systems and Cosmological Large Scale Structures
本文证明自引力N体系统中测地线聚焦产生引力焦散，并认为这是宇宙大尺度结构形成的机制，通过曲率分析及求解雅可比和雷乔杜里方程估算焦散时间尺度与密度对比度。
Self-gravitating darkon fluid with anisotropic scaling
将\cite{PRD}中引入的宇宙暗区流体模型（darkon流体）重新表述为只涉及物理相空间变量的修正模型。该模型的拉格朗日量不具有自由粒子极限，因此它所描述的粒子，暗子，只作为自引力流体存在。这darkon流体提出了一个动态实现的零质量伽利略代数扩展的各向异性膨胀对称与动力学指数$z=5/3$。该模型具有与\cite{PRD}相同的宇宙学相关解。我们还导出了早期宇宙学扰动的方程并确定了它们的解。此外，我们还讨论了增加高阶空间导数项的一些含义。
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of Minkowski spacetime. It allows one to exclude the existence of dynamically unstable, self-gravitating massive fields and, therefore, solves a long-standing open problem in General Relativity. By a significant extension of the Hyperboloidal Foliation Method they introduced in 2014, the authors establish global-in-time existence for the Einstein equations expressed as…
Chaos, Regularity, and Noise in Self-Gravitating Systems
本文总结了作者和他的合作者最近获得的一些新的、潜在重要的结果，这些结果影响了牛顿和广义相对论中与引力N体问题有关的各种问题。涉及的主题包括：（1）直接N体模拟及其解释，参考所观察到的初始条件对微小变化的指数不稳定性和“非暴力弛豫”现象（2）广义相对论的无碰撞玻尔兹曼方程的哈密顿结构，即，弗拉索夫-爱因斯坦系统;（3）“瞬态系综动力学”，即，，不可积平均场势中轨道集合的短时统计特征;（4）银河系动力学中常用的光滑势近似的结构稳定性。
Long-term Evolution of Stellar Self-Gravitating System away from the Thermal Equilibrium: connection with non-extensive statistics
特别注意最近假设的非广泛推广的玻尔兹曼-吉布斯统计的引入，我们研究的长期恒星动力学演化的自引力系统的时间尺度远长于两体弛豫时间。在绝热壁中的自引力N体系统中，我们证明了由Tsallis熵产生的准平衡序列，即所谓的恒星多面体，在表征远离Boltzmann-Gibbs平衡态的瞬态过程中起着重要的作用.
Exactly soluble model for self-gravitating D-particles with the wormhole
我们考虑了D粒子与CGHS引力场的耦合，通过引入奇异物质，得到了D粒子的精确虫洞几何和运动轨迹。初始静态虫洞背景在D粒子进入后由于几何学的经典反作用而变得不稳定，因此需要引入额外的奇异物质源来保证稳定性。然后，可穿越的虫洞几何形状自然出现，D粒子可以安全地穿过它。最后，我们讨论了虫洞喉道的动力学演化和D粒子的无质量极限。
Dynamical compact elastic bodies in general relativity
我们证明了局部存在的解决方案的爱因斯坦弹性方程，代表自引力，相对论性的弹性体与紧凑的支持。
Entropy of Radiation with Dynamical Gravity
本文通过添加DGP项在双全息黑弦模型中引入动力学引力，计算子区域纠缠熵，并分析大参数空间中哪些理论具有幺正熵演化及遵循Page曲线。
Theory of Newtonian self-gravitating stationary spherically symmetric systems
我们研究了与星系动力学有关的Vlasov-Poisson系统的球对称平衡态。我们将方程转化为一个正则的三维自治一阶常微分方程组，在紧闭包区域上，基于动力系统分析，我们得到了保证定态解具有有限质量和紧支集的定理。
The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and the Euler formulation of elasticity theory for spherically symmetric bodies introduced recently by the authors. Examples of elastic materials covered by the results of this paper are Saint Venant-Kirchhoff, John and Hadamard materials.
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