Piotr Bizoń, Arthur Wasserman
We give a very short proof that the vacuum Einstein equations in 4+1 dimensions have no cohomogeneity-two Bianchi IX continuously self-similar solutions.
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Critical behavior in vacuum gravitational collapse in 4+1 dimensions
我们证明了4+1维真空爱因斯坦方程允许径向对称的引力波存在。动力学自由度对应于正交于$(t,r)$平面的三个球体的变形。对这种波的引力坍缩进行了数值研究，结果表明，在黑洞形成的阈值处，这种波表现出离散的自相似II型临界行为。
Fractal Threshold Behavior in Vacuum Gravitational Collapse
我们给出了满足凝聚度2的三轴Bianchi IX型近似的五维真空Einstein方程的分形阈值行为的数值证据。换句话说，我们表明，蝴蝶翅膀的翻转可能会影响黑洞的形成过程。
Spherical vacuum and scalar collapse for the Starobinsky R^2 model is simulated. Obtained by considering the quantum-gravitational effects, this model would admit some cases of singularity-free cosmological spacetimes. It is found, however, that in vacuum and scalar collapse, when f' or the physical scalar field is strong enough, a black hole including a central singularity can be formed. In addition, near the central singularity, gravity dominates the repulsion from the potential, so that in some circumstances the Ricci scalar is pushed to infinity by gravity. Therefore, the semiclassical eff…
How to bypass Birkhoff through extra dimensions (a simple framework for investigating the gravitational collapse in vacuum)
公平地说，我们目前对黑洞的引力坍缩动力学的数学理解仅限于球对称的情况，事实上，即使在这种情况下，仍有许多东西有待学习。原因是爱因斯坦的方程只有当它们被简化为1+1维的偏微分方程系统时才变得容易处理。由于这一技术障碍，人们对纯引力波的坍缩知之甚少，因为根据伯克霍夫定理，真空中不存在球形坍缩。本文描述了一种新的5维及更高奇维真空爱因斯坦方程的相干性2对称约化，它避开了Birkhoff定理，并存在依赖于时间的渐近平坦解。我们认为该模型为研究真空中的引力坍缩动力学提供了一个有吸引力的1+1维几何环境。
A study of gravitational collapse with decaying of the vacuum energy
研究了$Λ$背景下尘埃暗物质星的引力坍缩。我们考虑两种不同的情况：第一，我们没有暗物质和暗能量耦合;第二，我们认为，$Λ$衰变的暗粒子。所采用的方法假设了一个修正的物质膨胀率，我们有一个黑洞的形成，因为，我们有一个明显的视界的形成。简要比较了用引力坍缩方法和线性标量微扰理论研究物质凝聚的过程。
We report on a numerical study of gravitational waves undergoing gravitational collapse due to their self-interaction. We consider several families of asymptotically flat initial data which, similar to the well known Choptuik's discovery, can be fine-tuned between dispersal into empty space and collapse into a black hole. We find that near-critical spacetimes exhibit behavior similar to the collapse of scalar field: For different families of initial data, we observe universal "echoes" in the form of irregularly repeating approximate scaled copies of the same piece of spacetime.
Gravitational Collapse of Vacuum Gravitational Field Configurations
本文证明了广义相对论中关于视视界存在性的一个定理，该定理同样适用于真空位形和物质位形。该定理用空间切片上一个区域的面积体积比的倒数来度量该区域的半径，用外曲率的某些分量的最小值$K_{\rm min}$来度量该区域的引力场的强度。该定理证明，如果半径乘以$K_{\rm min}$的乘积大于1，则必须形成一个视视界，这标志着黑洞的形成。
Formation of a Black String in a Higher Dimensional Vacuum Gravitational Collapse
我们给出了真空爱因斯坦方程的一个解，它代表了5维空间中引力波的坍缩。取决于波的焦距，坍缩的结果要么是一个被视界覆盖的黑弦，要么是一个可以被移除的裸奇点。
On vacuum gravitational collapse in nine dimensions
本文研究了九维爱因斯坦方程的两个相干解的真空引力坍缩。使用相结合的数值和分析方法，我们给出的证据表明，在这个模型中的Schwarzschild-Tangherlini黑洞是渐近稳定的。此外，我们还简要讨论了黑洞形成阈值时的临界行为。
Vacuum axisymmetric gravitational collapse revisited: preliminary investigation
本文重新探讨真空轴对称引力坍缩，提出爱因斯坦方程的新表述及线性化近似，并识别在黑洞形成阈值处实现数值稳定演化的关键问题，为验证Abrahams和Evans的经典结果迈出第一步。
Some remarks on the horizon in the dust cloud collapse
研究通过扩张函数探讨孤立尘埃云坍缩中的视界存在性，发现远离引力奇点区域存在视界，表明奇点被覆盖，但该方法在奇点附近可能受限。
Radiative gravastar with thermal spectrum; Sudden vacuum condensation without gravitational collapse
该研究在引力真空凝聚形成引力真空星的玩具模型中，验证了新形成的引力真空星会因内部几何结构变化发出具有德西特核Gibbons-Hawking温度的热辐射，深化了对其热辐射机制的理解。
It is given a simple proof of the collapse conjecture for a diagonal Bianchi type-IX vacuum space-time. It is shown that the codimension of the infinity stable attractor, restricted to the anisotropy plane, is not zero, thus proving that "escape along a channel" is impossible.
Codimension-two critical behavior in vacuum gravitational collapse
本文研究了满足凝聚度2的三维Bianchi IX方程组在黑洞形成阈值处的临界行为。利用这个模型中存在的离散对称性，我们预测存在一个余维2吸引子。这一预测证实了数值和余维两个吸引子被确定为一个离散的自相似的解决方案，两个不稳定的模式。
In this paper, we discuss the Higgs vacuum stability around evaporating black holes. We provide a new approach to investigate the false vacuum decay around the black hole and clearly show how vacuum fluctuations of the Higgs induce a gravitational collapse of the vacuum. Furthermore, we point out that the backreaction of the Hawking radiation can not be ignored and the gravitational vacuum decay is exponentially suppressed. However, a large number of the evaporating (or evaporated) primordial black holes threaten the existence of the Universe and we obtain a new upper bound on the evaporating …
Quantum Effects of the Conformal Anomaly in a 2D Model of Gravitational Collapse
本文在二维引力坍缩模型中通过引入标量共形场研究量子共形反常的宏观效应，发现非真空初始态可导致黑洞视界上的半经典应力张量任意增大，从而抑制Hawking辐射并引发显著反作用，且此类初始条件出现的概率量级为1。
Vacuum polarisation and regular gravitational collapse
本研究针对半经典引力框架下的黑洞形成与演化问题，在多种存在或接近形成俘获区的时空中分析应力-能量张量算符的真空期望值，以探究对应场景的时空半经典动力学特性。
A Remark on Boundary Effects in Static Vacuum Initial Data sets
设（M，g）是具有非空紧边界的渐近平坦静态真空初值集。在假设（M，g）的边界平均曲率为零的条件下，我们证明了（M，g）与Schwarzschild时空的类空切片等距，从而推广了Bunting和Masood-ul-Alam的经典结果.在边界具有常的正平均曲率且满足稳定性条件的情况下，得到了（M，g）的ADM质量的一个由边界面积和平均曲率表示的上界.我们的讨论是由Bartnik的准局域质量定义的动机。
Critical collapse of vacuum spacetimes: Nakamura wave initial data
采用Nakamura构造的初始数据，数值模拟轴对称真空引力波的临界坍缩，发现阈值解近似离散自相似但不精确，且无唯一临界解。
We investigate the virialization of cosmic structures in the framework of flat FLRW cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, "turn around" and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, $Λ=Λ(H)$. A particularly well motivated model of this type is the so-called quantum field vacuum, in which $Λ(H)$ is a quadratic function, $Λ(H)=n_0+n_2\…
The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of $\hbar$, it is not straight forwardly possible to find global conformally compactified coordinates and to construct the Penrose diagram. Therefore, radial in- and outgoing light rays are studied to extract the causal features and sketch a causal diagram. It was found that the eternal metric [2], which is the vacuum solution of the collapse model, has a causal horizon. However, in the collapsing case light rays travel …
Remarks on stationary vacuum black holes
本文完成稳态解析真空黑洞无毛定理的证明，并展示无需解析性即可定义表面引力与角速度，且近视界几何为克尔型。
The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. It is a non-trivial question to ask whether (and to what extent) there exist equivalently general conditions under which one expects discrete spacetimes to become geodesically incomplete, and how these conditions might differ from those in the continuum. This article builds upon previ…
Within the framework of inflationary models that incorporate a spontaneous reduction of the wave function for the emergence of the seeds of cosmic structure, we study the effects on the primordial scalar power spectrum by choosing a novel initial quantum state that characterizes the perturbations of the inflaton. Specifically, we investigate under which conditions one can recover an essentially scale free spectrum of primordial inhomogeneities when the standard Bunch-Davies vacuum is replaced by another one that minimizes the renormalized stress-energy tensor via a Hadamard procedure. We think…
Gravitational Collapse of Inhomogeneous Dust in (2+1) Dimensions
本文研究了具有宇宙学常数的（2+1）维球对称非均匀尘埃的引力坍缩。我们得到了内部度量的解析表达式。我们将溶液与真空外部相匹配。通过分析出射径向零测地线，讨论了奇点的性质。我们研究的形成过程中的陷获表面的崩溃。
Remarks on vacuum fluctuations around a spinning cosmic string
本文应用点分裂方法研究了自旋宇宙弦非全局双曲背景中的真空涨落。通过去除Minkowski贡献实现重整化，表明文献中的格林函数虽然满足通常的格林函数方程，但会导致病态的物理结果。
Beyond the Unruh vacuum: multi-time correlations in black hole collapse and evaporation
本文通过二维引力坍缩与蒸发模型，证明晚期多时间量子场关联包含依赖坍缩前状态的贡献，表明多时间关联是霍金辐射中信息的载体，单时间可观测量的信息悖论表述不完整。
Remarks on Papapetrou Class of Vacuum Solutions of Einstein Equations
本文给出了真空爱因斯坦场方程的一类轴对称解，其中包括作为特例的Papapetrou解，证明了所导出的解描述了非零质量源的外部轴对称引力场。得到了这类函数的通解。作为物理应用的一个例子，从引力场真空方程的Papapetrou解出发，得到了线引力场外的时空度规。
Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of global prolongation of the metric is still open. On the other hand the so called matter-vacuum matching problem, particularly as the source problem for the Kerr metric, has been discussed by several authors. This can be regarded as the approach to the same open problem in the opposite direction. We give a remark on this open problem.
We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in $R^2$ gravity. We make our calculations using dimensionless time with characteristic timescale $t_{g}\sim (Gρ)^{-1/2}$ where $ρ$ is a density of collapsing matter. The cases of matter, radiation and stiff matter are considered. We also account the possible existence of vacuum energy and its influence on gravitational collapse. In a case of $R^2$ gravity we have additional degree of freedom for initial conditions of collapse. For barotropic equation of…
A Remark on Non-conformal Non-supersymmetric Theories with Vanishing Vacuum Energy Density
讨论了微扰论中真空能量密度为零的非共形非超对称大N规范理论。这些规范理论可以通过嵌入轨道折叠时空的IIB型D3-膜的场论极限得到。我们还讨论了这个设置中的重力。
Crunch from AdS bubble collapse in unbounded potentials
本文研究无界真真空势中标量场理论中零能量AdS气泡的坍缩过程，证明其会在达到真真空前形成被表观视界遮蔽的类空曲率奇点，且无需势有下界。
Dark energy models based on f(R) theory have been extensively studied in literature to realize the late time acceleration. In this paper, we have chosen a viable f(R) model and discussed its effects on the dynamical instability of expansionfree fluid evolution generating a central vacuum cavity. For this purpose, contracted Bianchi identities are obtained for both the usual matter as well as dark source. The term dark source is named to the higher order curvature corrections arising from f(R) gravity. The perturbation scheme is applied and different terms belonging to Newtonian and post Newton…
Presently, the inclusion of the vacuum energy in the energy momentum tensor, and the inclusion of the extra dimensions in the spacetime, can not be rule out of the research in gravitation. In this work we study the influence of the vacuum energy in the collapse process of a stellar fluid, and consequently for the cosmic censorship conjecture, considering a homogeneous and isotropic spacetime with arbitrary number of dimensions. We discuss the active gravitational mass of the black hole formed, where the vacuum energy and the number of dimensions has a crucial role in the process.
After collapse: On how a physical vacuum can change the black hole paradigm
该研究以自由量子标量场为代理，分析反应性真空下的球对称引力场，发现静态超致密恒星构型可被误认作黑洞，且黑洞内视界或在霍金蒸发前与外视界相遇，改变黑洞范式。
Gauge-invariant and coordinate-independent perturbations of stellar collapse II: matching to the exterior
在本系列的第一篇论文中，我们构造了含时球对称完美流体时空的完全规范不变线性扰动的演化方程。这种形式主义的一个关键应用是坍缩恒星的内部。在这里，我们推导出在恒星表面的边界条件，匹配的内部扰动著名的真空史瓦西时空的恒星外的扰动。
We extend the Induced Matter Theory of gravity (IMT) to 5D curved spacetimes by using the Weitzenböck representation of connections on a 5D curved spacetime. In this representation the 5D curvature tensor becomes null, so that we can make a static foliation on the extra noncompact coordinate to induce in the Weitzenböck representation the Einstein equations. Once we have done it, we can rewrite the effective 4D Einstein equations in the Levi-Civita representation. This generalization of IMT opens a huge window of possible applications for this theory. A pre-big bang collapsing scenario is expl…
We report on critical phenomena in the gravitational collapse of electromagnetic waves. Generalizing earlier results that focused on dipole electromagnetic waves, we here compare with quadrupole waves in axisymmetry. We perform numerical simulations of dipole and quadrupole wave initial data, fine-tuning both sets of data to the onset of black hole formation in order to study the critical solution and related critical phenomena. We observe that different multipole moments have different symmetries, indicating that the critical solution for electromagnetic waves cannot be unique, at least not g…
The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically symmetric space-time due to Einstein--Rosen using the Darmois matching conditions. It is found that the radial pressure of the anisotropic perfect fluid is non-zero on the boundary surface and is related to the components of shear viscosity. As a result, there is formation of gravitational waves outside the collapsing matter.
Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves
本研究通过数值模拟探究真空轴对称引力波坍缩的黑洞形成阈值临界现象，对比四极与十六极Teukolsky波初始数据的演化结果，发现两类阈值解均具近似离散自相似性且存在差异，为真空引力波坍缩无普适临界解提供了新证据。
Remarks on evolution of space-times in 3+1 and 4+1 dimensions
利用非小扰动的双曲初始数据，在4+1维空间中构造了一大类真空时空。这些时空是未来测地线完备的，平滑到它们未来的零无穷大，并作为真空时空通过它们的柯西视界延伸。降维给出了在3+1维中具有相同性质的非真空时空。
Quantum vacuum effects on the formation of black holes
本文研究真空极化与共形反常产生的量子场反作用对薄尘埃壳坍缩的影响，揭示双视界结构及奇点或规则黑洞形成的条件。
Vacuum energy problem in anti-de Sitter space
针对反德西特空间中负真空能导致宇宙坍缩为奇点的问题，提出与曲率标量非最小耦合的标量场的真空能补偿动力学机制，经计算可避免奇点并驱动宇宙幂律膨胀。
Dynamics of false vacuum bubbles with trapped particles
本研究通过模拟泡-粒子系统，发现粒子在泡壁的质量增加及其反作用可减缓或逆转假真空泡的坍缩，从而降低其形成黑洞的可能性。
In this thesis the universal collapse of vacuum Brill waves is demonstrated numerically and analytically. This thesis presents the mathematical and numerical methods necessary to regularise and evolve Brill Gravitational Waves in spherical polar coordinates. A Cauchy ADM formulation is used for the time evolution. We find strong evidence that all IVP formulations of pure vacuum Brill gravitational waves collapse to form singularities/black holes, and we do not observe critical black hole mass scaling phenomena in the IVP parameter phase space that has been characterised in non-vacuum systems. …
Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation…
We reexamine the gravitational collapse of rotating neutron stars to black holes by new 3+1 numerical relativity simulations employing the Z4c formulation of Einstein equations, the moving puncture gauge conditions, and a conservative mesh refinement scheme for the general relativistic hydrodynamics. The end state of the collapse is compared to the vacuum spacetime resulting from the evolution of spinning puncture initial data. Using a local analysis for the metric fields, we demonstrate that the two spacetimes actually agree. Gravitational waveforms are analyzed in some detail. We connect the…
Spherically Symmetric Scalar Field Collapse: An Example of the Spacetime Problem of Time
球对称的正则形式主义，最初由Kuchasyngy开发来描述真空Schwarzschild黑洞，扩展到包括球对称，无质量，标量场源。通过引入ADM质量作为相空间的正则坐标，我们发现耦合系统的超哈密顿量和超动量约束大大简化。然而，尽管这种简化，很难找到一个功能的时间形式主义的理论。首先，一旦球对称物质与引力耦合，在真空理论中扮演时间角色的位形变量就不再是时空标量。第二，虽然可以对一组新的变量进行正则变换，从而可以求解超哈密顿和超动量约束，但新的时间变量也不能是时空标量。因此，我们的解决方案受到所谓的{ \it时空时间问题}的影响。提出了一个时间变量{ \it是}时空标量的候选者.把这个变量变成一个典型的坐标相空间的问题进行了讨论。
The Quantum Collapse and the Birth of a New Universe
引力坍缩和新宇宙的诞生是根据量子力学来考虑的。从物质湮灭到坍缩的崩溃和从通货膨胀到创造的宇宙诞生的物质被认为是过渡。新宇宙的产生发生在另一个时空中，因为在事件视界之外，时间坐标对于外部观察者来说是不可扩展的。只有对于微洞，才能得到这种产生的合理概率。坍缩的致密天体，如恒星、类星体和活动星系核，其大部分质量仍被限制在真空态附近的势阱中。
Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation…
Some remarks on the thermal and vacuum fluctuations of a massive scalar field
最近我们获得了Rindler楔中质量标量场的热涨落。作为副产品，由均匀加速观察者看到的闵可夫斯基真空涨落已经被确定，并与由惯性观察者看到的相同场的相应闵可夫斯基热涨落相遇。由于以前工作中的一些计算没有详细说明，它们提出了一些重要的微妙之处，所以在这里明确地完成。这些微妙之处与某些参数相关积分的首阶行为有关。一些领先的阶展开使用Riemann-Lebesgue引理。
Numerical studies of gravitational collapse in isotropic coordinates have recently shown an interesting connection between the gravitational Lagrangian and black hole thermodynamics. A study of the actual spacetime was not the main focus of this work and in particular, the rich and interesting structure of the interior has not been investigated in much detail and remains largely unknown. We elucidate its features by performing a numerical study of the spacetime in isotropic coordinates during gravitational collapse of a massless scalar field. The most salient feature to emerge is the formation…
Late-time particle creation from gravitational collapse to an extremal Reissner-Nordstrom black hole
研究了由引力坍缩形成的极端Reissner-Nordstrom（RN）黑洞的粒子创生行为.我们明确地计算粒子流与无质量标量场在崩溃后的后期时间。我们的结果表明，在任何自发产生的波包的粒子的期望数量接近零的速度比任何时间的逆幂。这一结果证实了极端黑洞不发射粒子的传统观点。我们还计算了1+1 RN黑洞的应力能量张量的期望值，并表明它也在后期下降到零。其他作者以前的工作提供了一些意见。
Critical phenomena in the collapse of gravitational waves
针对真空引力波坍缩临界现象难以观测的问题，研究通过三次独立数值模拟首次获得高度吻合结果，发现该过程不具备普适性，仅部分初始数据族存在近似自相似性。
We reinvestigate the emission of Hawking radiation during gravitational collapse to a black hole. Both CGHS collapse of a shock wave in (1+1)-dimensional dilaton gravity and Schwarzschild collapse of a spherically symmetric thin shell in (3+1)-dimensional gravity are considered. Studying the dynamics of in-vacuum polarization, we find that a multi-parametric family of out-vacua exists. Initial conditions for the collapse lead dynamically to different vacua from this family as the final state. Therefore, the form of the out-vacuum encodes memory about the initial quantum state of the system. Wh…
Simulations of gravitational collapse in null coordinates: II. Critical collapse of an axisymmetric scalar field
该研究首次用类光坐标数值模拟非球对称轴对称标量场的临界坍缩，证实中等非球对称初态下Choptuik解仍存在，对比了前人结果并指出未来大偏离球对称研究需更换径向坐标。
A brief remark on Unruh effect and causality
Unruh效应指出，闵可夫斯基时空上的量子场论的真空，对于一个永恒的匀加速观测者来说，看起来像是一个热态。适应非永恒的情况会引起一个严重的问题：如果真空的热化取决于观察者的寿命，那么原则上最新的能够从温度的测量中推断出它的寿命。这个简短的说明旨在强调时间-能量不确定性关系允许在不破坏因果关系的情况下使Unruh效应适应非永恒的观察者。特别是，我们表明，我们的适应-钻石的温度-Bisognano-Wichman的方法Unruh效应是因果关系上可以接受的。本说明自成一体，但作为对gr-qc/0212074的补充以及对gr-qc/0306022的评论，它是完全有意义的。
Covariant LTB collapse in models of loop quantum gravity
本文在含协变完整修正的涌现修正引力中分析临界束缚 LTB 坍缩，证明普适坍缩仍产生物理奇点，并消除同类修正真空时空中的反弹。
Some Remarks on Gravitational Global Monopoles
本文主要用解析的方法导出了静态引力球单极子中希格斯场最大真空值的精确关系式$η_{max}=\sqrt{3/8π}$。对于这个值，全局解与在Higgs场为零时得到的de Sitter解分叉。此外，我们还分析了解的稳定性。
Thermal duality is a relationship between the behaviour of heterotic string models of the $E(8)x E(8)$ or $SO(32)$ types at inversely related temperatures, a variant of T duality in the Euclidean regime. This duality would have consequences for the nature of the Hagedon transition in these string models. We propose that the vacuum admits a family of deformations in situations where there are closed surfaces of constant area but high radial acceleration (a string regularized version of a Penrose trapped surface), such as would be formed in situations of extreme gravitational collapse. This woul…
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