Leo Brewin, Jules Kajtar
We present test results for the smooth lattice method using an Oppenheimer-Snyder spacetime. The results are in excellent agreement with theory and numerical results from other authors.
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The Oppenheimer-Snyder solution models a homogeneous round dust cloud collapsing to a black hole. Inside its event horizon there is a region through which trapped surfaces pass. We try to determine exactly where the boundary of this region meets the centre of the cloud. We present explicit examples of the relevant trapped (topological) spheres; they extend into the exterior vacuum region, and are carefully matched at the junction between the cloud and the vacuum.
We consider a scenario of the gravitational collapse of the Oppenheimer-Snyder dust cloud with spatially constant matter density. Given a closed two-surface within the star, three versions of the quasi-local energy are investigated. We show that, during the collapse, (i) the Geroch energy of the surface is nonpositive and increases to zero; (ii) the Hawking energy of the surface is monotonically increasing and approaches to the Hayward energy of the initial surface; and (iii) the Hayward energy of the surface is conserved and remains positive. These results have no restrictions on the topology…
Higher-dimensional quantum-corrected Oppenheimer-Snyder model with a cosmological constant
将高维量子Oppenheimer-Snyder模型推广至含宇宙学常数情形，在AdS情况下研究扩展相空间热力学，发现量子修正使小黑洞温度趋于零并引发额外相变。
Besides the singularity problem, the famous Oppenheimer and Snyder solution is discovered to be of deficiency in two aspects: the internal Friedmann space-time does not have the inherent symmetry and cannot connect to the external Schwarzschild space-time. So the process of gravitational collapse described by this solution is doubtful. The deficiency, together with the singularity problem, result from the imperfection of the field theory in continuous space-time, which is expressed by the infinite precision function theory. The space-time structure of the Oppenheimer and Snyder dust ball is fo…
Moving-puncture coordinates are commonly used in numerical simulations of black holes. Their properties for vacuum Schwarzschild black holes have been analyzed in a number of studies. The behavior of moving-puncture coordinates in spacetimes containing matter, however, is less well understood. In this paper we explore the behavior of these coordinates for Oppenheimer-Snyder collapse, i.e., the collapse of a uniform density, pressureless sphere of dust initially at rest to a black hole. Oppenheimer-Snyder collapse provides a stringent test of the singularity-avoiding properties of moving-punctu…
Assessing EMRI Detectability of the Rotating Quantum Oppenheimer-Snyder Black Hole
本文通过自洽演化计算引力波退相，研究量子引力对EMRI的影响，发现量子效应在LISA上可探测，但旋转会抑制这些信号。
The black hole shadow of quantum Oppenheimer-Snyder-de Sitter spacetime
本文研究圈量子引力精确黑洞解推广至旋转情形后的零测地线与黑洞阴影，以比较不同理论影响并提供检验修正引力理论的新方法。
Higher-dimensional quantum Oppenheimer-Snyder model
研究高维时空的量子奥本海默-斯奈德模型，通过连接条件得到量子修正史瓦西黑洞，发现坍缩中量子反弹可避免奇点，量子修正对标量扰动频率的影响因维度而异，且改变了黑洞热力学性质，引入额外相变。
The Oppenheimer-Snyder model, which describes the gravitational collapse of a ball of dust, can be used to model thermalization of strongly coupled systems using the AdS/CFT-duality. It can be used as an alternative to the previously widely used thin-shell model in the context of holographic thermalization. We solve the dynamics of the Oppenheimer-Snyder collapse in asymptotically AdS space-times and compute the two-point function of a boundary spectator field in the geodesic approximation. As a comparison we perform the same computation in the thin-shell model and discover oscillatory solutio…
The Lovelock gravity extends the theory of general relativity to higher dimensions in such a way that the field equations remain of second order. The theory has many constant coefficients with no a priori meaning. Nevertheless it is possible to reduce them to two, the cosmological constant and Newton's constant. In this process one separates theories in even dimensions from theories in odd dimensions. In a previous work gravitational collapse in even dimensions was analysed. In this work attention is given to odd dimensions. It is found that black holes also emerge as the final state of gravit…
Quantum Oppenheimer-Snyder primordial black holes as all the dark matter
研究量子奥本海默-辛格原初黑洞作为暗物质候选者，发现其温度和灰体因子不同于Schwarzschild情况，抑制霍金辐射，缓解γ射线约束，扩大允许的原初黑洞质量范围。
We present a consistent canonical formulation of the flat Oppenheimer-Snyder model, including the Schwarzschild exterior. The switching between comoving and stationary observer is realized by promoting the coordinate transformation between dust proper time and Schwarzschild-Killing time to a canonical one. This leads to two different forms of the Hamiltonian constraint, both (almost) deparameterizable with regard to one of these times. A preliminary quantization of these constraints reveals a consistent picture for both observers: the singularity is avoided by a bounce.
Constraints on quantum Oppenheimer-Snyder black holes with eccentric extreme mass-ratio inspirals
本文在圈量子引力框架下模拟偏心极端质量比旋进的轨道演化与引力波信号，证明 LISA 可分辨约 $10^{-5}$ 的量子修正并给出强于黑洞阴影观测的约束。
We shall study the formation of a particular class of regular black holes from the gravitational collapse of a massive star. The inside geometry is described by spatially flat Friedmann-Robertson-Walker metric and the stellar matter is distributed uniformly without any pre-assumption about its equation of state. Our model is a generalization of Oppenheimer-Snyder collapse for regular black holes. We have obtained the density and pressure of star by applying the condition of smooth joining of metrics at the freely falling surface of star. Specifying the regular black holes to Hayward and Bardee…
The Upper Bound of Event Horizon Formation Time in Generalized Oppenheimer-Snyder Collapse
该研究在广义奥本海默-辛德尔坍缩中证明了事件视界形成时间的最大上限，扩展了传统黑洞不等式到时间设定。
Quantum Oppenheimer-Snyder black hole evaporation and its fate
本文研究了量子奥本海默-辛内尔黑洞的蒸发过程，发现量子引力效应在晚期导致残余形成，非最小耦合情况下残余稳定性取决于耦合常数ξ的值。
By considering the quantum Oppenheimer-Snyder model in loop quantum cosmology, a new quantum black hole model whose metric tensor is a suitably deformed Schwarzschild one is derived. The quantum effects imply a lower bound on the mass of the black hole produced by the collapsing dust ball. For the case of larger masses where the event horizon does form, the maximal extension of the spacetime and its properties are investigated. By discussing the opposite scenario to the quantum Oppenheimer-Snyder, a quantum Swiss Cheese model is obtained with a bubble surrounded by the quantum universe. This m…
Quantum Oppenheimer-Snyder Black Holes with a Cloud of Strings Surrounded by Perfect Fluid Dark Matter
本研究探讨了量子修正、弦云和暗物质对黑洞几何结构与热力学特性的影响，并通过光子球和阴影分析提出观测区分方法。
Massive particles tunneling from quantum Oppenheimer-Snyder black holes and black hole entropy
本研究用Parikh-Wilczek隧穿方法分析有质量标量粒子从量子奥本海默-斯奈德黑洞的隧穿，得到含圈量子引力修正的发射率，推导的黑洞熵含对数修正，符合量子引力普适熵公式。
We construct two reduced quantum theories for the Oppenheimer-Snyder model, respectively taking the point of view of the comoving and the exterior stationary observer, using affine coherent states quantization. Investigations of the quantum corrected dynamics reveal that both observers can see a bounce, although for the exterior observer certain quantization ambiguities have to be chosen correctly. The minimal radius for this bounce as seen from the stationary observer is then shown to always be outside of the photon sphere. Possible avenues to lower this minimal radius and reclaim black holes…
Quasinormal Modes, Greybody Factors and Rigorous Bounds for Quantum Oppenheimer-Snyder Black Hole with Quintessential Dark Energy and a String Clouds
研究量子奥本海默-辛德勒黑洞在本质暗能量和弦云影响下的准正常模式与灰体因子，通过WKB近似方法计算并分析其参数影响。
Painlevé-Gullstrand coordinates discontinuity in the quantum Oppenheimer-Snyder model
本文研究了量子 Oppenheimer-Snyder 模型中 Painlevé-Gullstrand 坐标下的度规不连续性问题，指出该不连续性仅为坐标效应，几何可连续过渡至膨胀的白洞阶段且无激波产生。
Josephson interferometry in an Oppenheimer--Snyder-like scale-dependent black-hole spacetime
本研究针对类奥本海默-斯奈德标度依赖黑洞时空构建协变框架，分析约瑟夫森输运、干涉及噪声，推导相关方程、关系与灵敏度界限，为黑洞相关超导干涉测量提供理论支撑。
Charged quantum Oppenheimer-Snyder model
本文基于非线性电动力学，研究带电量子修正黑洞与尘埃球的匹配问题，探讨量子效应修正的 Schwarzschild 度规及薄壳振荡特性。
Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model
本研究通过数值光线追踪和半解析方法，揭示了量子奥本海默-斯奈德模型中裸奇点与黑洞的光学特征及热力学性质，并建立了光子环观测与热力学稳定性间的联系。
Canonical-Ensemble Stability of the Quantum Oppenheimer-Snyder Black-Hole Exterior
本研究在正则系综框架下分析量子Oppenheimer-Snyder黑洞外部的热力学，发现近极端与大黑洞分支的鞍点结构，并在特定视界尺度处出现戴维斯型局部稳定性转变，澄清了已知结果的适用域。
Quantum system ascribed to the Oppenheimer-Snyder model of massive star
本文通过积分量子化方法对Oppenheimer-Snyder黑洞模型进行量子化，平等处理时空坐标，从而消除经典曲率奇异性，并得到具有有限反弹时间的量子黑洞及Schwarzschild奇点的量子消解。
From classical to quantum Oppenheimer-Snyder model: non-marginal case
本文给出了一般 Oppenheimer-Snyder 模型的正则表述，通过 ACSQ 方法实现量子化，证明量子修正轨迹能以反弹取代经典奇点，且共动与静止观测者均观测到此反弹坍缩行为。
The quasinormal modes, pseudospectrum and time evolution of Proca fields in quantum Oppenheimer-Snyder-de Sitter spacetime
本文研究了量子修正de Sitter黑洞背景下Proca场的准正规模式与时间演化，通过超曲面框架和伪谱方法揭示量子修正、宇宙学常数及Proca质量对模式不稳定性的不同影响，并确认无幂律晚期尾部。
Violation of weak cosmic censorship by the Oppenheimer-Snyder collapse
本研究探讨利用奥本海默-斯奈德坍缩模型违反弱宇宙监督猜想的可能性，发现现有模型无法物理实现，但为构造性研究宇宙监督性质及修正引力模型提供新窗口。
Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time
本文推广了奥本海默-辛内模型，研究了引力坍缩中视界形成时间的临界条件及影响因素。
Quasinormal Frequencies of Fields with Various Spin in the Quantum Oppenheimer-Snyder Model of Black Holes
本文研究量子 Oppenheimer-Snyder 黑洞中不同自旋场的准正频，结合时域积分与 WKB 方法发现量子参数显著降低阻尼率，并验证 eikonal 极限下的零测地线对应。
This article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models : if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or…
Rainbow Oppenheimer-Snyder collapse and the entanglement entropy production
本文在圈量子宇宙学框架下用彩虹度规方法研究Oppenheimer-Snyder尘埃球坍缩，确定整体时空结构并计算纠缠熵，发现模型定性类似Reissner-Nordström黑洞且仍含奇点，进而讨论其对黑洞信息丢失悖论及场景可行性的影响。
Quantum Oppenheimer-Snyder models in loop quantum cosmology with Lorentz term
本文提出一种包含洛伦兹项的量子黑洞模型，通过修正度规和热力学性质，揭示了环量子引力对黑洞稳定性及相变的影响。
We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a FLRW spacetime with arbitrary perturbations. The matching hypersurface is also perturbed arbitrarily and, in all cases, the perturbations are decomposed into scalars using the Hodge operator on the sphere. This allows us to write down the matching conditions in a compact way. In particular, we find that the existence of a perturbed (rotating, stationary and vacuum) Schwarzschild cavity in a perturbed FLRW universe forces the cosmological pertur…
In this paper we analyse the boundedness of solutions $ϕ$ of the wave equation in the Oppenheimer--Snyder model of gravitational collapse in both the case of a reflective dust cloud and a permeating dust cloud. We then proceed to define the scattering map on this space-time, and look at the implications of our boundedness results on this scattering map. Specifically, it is shown that the energy of $ϕ$ remains uniformly bounded going forward in time and going backwards in time for both the reflective and the permeating cases, and it is then shown that the scattering map is bounded going forward…
We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with respect to the one predicted by general relativity. Moreover, the equivalence principle is violated. If one assumes that Snyder mechanics is valid also for macroscopic systems, these results impose strong constraints on the value of the coupling parameter of the Snyder model.
A family of effective actions in Hamiltonian form is derived for a self-gravitating sphere of isotropic homogeneous dust. Starting from the Einstein-Hilbert action for barotropic perfect fluids and making use of the symmetry and equation of state of the matter distribution we obtain reduced actions for two canonical variables, namely the radius of the sphere and its ADM energy, the latter being conserved along trajectories of the former. These actions differ by the value of the (conserved) geodesic energy of the radius of the sphere which defines (disconnected) classes of solutions in correspo…
The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued Euler characteristics of lower dimensions. The theory has many constant coefficients apparently without any physical meaning. However, it is possible, in a natural way, to reduce to two (the cosmological and Newton's constant) these several arbitrary coefficients, yielding a restricted Lovelock gravity. In this process one separates theories in even dimensio…
Tidal forces in the quantum Oppenheimer--Snyder black hole
本文研究量子奥本海默-斯奈德黑洞中自由下落粒子的潮汐力，揭示其与史瓦西黑洞的差异，表明量子修正可消除奇点，极端值以上几何无视界且变形历史暴露给遥远观测者。
Oppenheimer-Snyder Collapse in f(R) Gravity : Stalemate or Resolution?
基于f(R)引力，研究Oppenheimer-Snyder坍缩问题，发现常规Ricci-flat外部解被排除，但通过限制外部物质形式，发现f(R)导数需满足特定条件，限制了外部解的可能，使坍缩问题在局部可逆情况下仍无明确解决。
Asymmetric Quantum Oppenheimer-Snyder Collapse
本研究在圈量子宇宙学框架下，分析尘埃球坍缩过程中出现的物理激波，推导真空 sector 的类似史瓦西线元，首次确立该框架内完全动力学的正则黑洞形成。
Unlike general relativity, scalar-tensor theories of gravity predict scalar gravitational waves even from a spherically symmetric gravitational collapse. We solve numerically the generation and propagation of the scalar gravitational wave from a spherically symmetric and homogeneous dust collapse under the approximation that we can neglect the back reaction of the scalar wave on the space-time, and examine how the amplitude, characteristic frequency and wave form of the observed scalar gravitational wave depend on the initial radius and mass of the dust and parameters contained in the theory. …
Observational properties of magnetized quantum Oppenheimer-Snyder black holes
该研究计算了外部磁场中量子 Oppenheimer--Snyder 黑洞的薄吸积盘性质与俘获截面，发现量子参数影响微弱而磁场显著增强辐射效率，且阴影仅由量子参数决定。
Classification of Oppenheimer-Snyder Collapse: Singular, Bouncing, and Soft-Landing Scenarios
研究奥本海默-斯奈德引力坍缩与一般静态、球对称外部时空匹配情况，通过分析确定导致黑洞出现表观视界最小值和反弹的条件，将坍缩分为奇异、反弹、软着陆三类，结果符合彭罗斯强宇宙审查猜想。
Oppenheimer-Snyder type collapse for a collisionless gas
该研究针对无碰撞气体的引力坍缩问题，在Painlevé-Gullstrand坐标下证明了Einstein-Vlasov系统正则解的局部存在唯一性与延拓准则，证实近似尘埃初始数据的无碰撞气体坍缩仍会形成黑洞，弥补了尘埃模型零压强的局限。
Regular black holes from Oppenheimer-Snyder collapse
本文将 D≥5 维含高曲率修正理论中的正则黑洞解释为无压尘埃星 Oppenheimer-Snyder 型坍缩与反弹的结果，并证明同类理论中的 FLRW 宇宙奇点也由平滑反弹替代。
The only instance when the General Relativistic (GTR) collapse equations have been solved (almost) exactly to explicitly find the metric coefficients is the case of a homogeneous spherical dust (Oppenheimer and Snyder in 1939 in Phy. Rev. 56, 455). The equation (37) of their paper showed the formation of an event horizon for a collapsing homogeneous dust ball of mass M in that the circumference radius the outermost surface, r_b = r_0= 2M in a proper time proportional to r_0^{-1/2} in the limit of large Schrarzschild time t= infinity. But Eq.(37) was approximated from the Eq. (36) whose essenti…
On a cosmological Oppenheimer-Snyder model: matching McVittie and FLRW spacetimes
该研究探讨McVittie时空与FLRW时空沿任意超曲面平滑匹配的条件，证明匹配系统的解在未来整体存在唯一，得出McVittie时空全局无各向同性源的结论。
We report an investigation of the Snyder noncommutative spacetime and of some of its most natural generalizations, also looking at them as a powerful tool for comparing different notions of dimensionality of a quantum spacetime. It is known that (generalized-)Snyder noncommutativity, while having rich off-shell implications (kinematical Hilbert space), does not affect on-shell particles (physical Hilbert space), and we argue that physically meaningful notions of dimensionality should describe such spacetimes as trivially four-dimensional, without any running with scales. By studying the thermo…
The Tolman-Oppenheimer-Snyder description gives exact analytical solutions for an Einstein-matter system describing total gravitational collapse of a zero-pressure perfect-fluid sphere, representing a massive star which has exhausted its nuclear fuel. The star collapses to a point of infinite density within a finite comoving proper time interval $[0,t_{*}]$, and the exterior metric matches the Schwarzchild black hole metric. The description is re-expressed in terms of a 'density function' $u(t)=(ρ(t)/ρ_{o}))^{1/3}=R^{-1}(t)$ for initial density $u_{0}=R^{-1}(0)=1$ and radius $R(0)$, whereby th…
Gravitational collapse is still poorly understood in the context of $f(R)$ theories of gravity, since the Oppenheimer-Snyder model is incompatible with their junction conditions. In this work, we will present a systematic approach to the problem. Starting with a thorough analysis of how the Oppenheimer-Snyder construction should be generalised to fit within metric $f(R)$ gravity, we shall subsequently proceed to explore the existence of novel exterior solutions compatible with physically viable interiors. Our formalism has allowed us to show that some paradigmatic vacuum metrics cannot represe…
Alternative approaches to the study of the quantum-gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetim…
Joint Constraints on Quantum Oppenheimer--Snyder Black Holes from High-Frequency Quasi-Periodic Oscillations in X-ray Binary Systems and the S2 Star Orbit
本研究通过X射线双星QPO和S2轨道约束量子修正OS黑洞的有效参数α，发现最小视界质量并给出α=0.22±0.10的一致范围。
We show that the UV-regime at the Lifshitz point $z=3$ is equivalent to work with a momenta manifold whose topology is the same as that of an $AdS_2\times S^2$ space. According to Snyder's theory, curved momentum space is related to non-commutative quantized spacetime. In this sense, our analysis suggests an equivalence between Horava-Lifshitz and Snyder's theory.
We study the effects of relative locality dynamics in the case of the Snyder model. Several properties of this model differ from those of the widely studied $κ$-Poincaré models: for example, in the Snyder case the action of the Lorentz group is preserved, and the composition law of momenta is deformed by terms quadratic in the inverse Planck energy. From the investigation of time delay and dual curvature lensing we deduce that, because of these differences, in the Snyder case the properties of the detector are essential for the observation of relative locality effects. The deviations from spec…
A metric with a Lorentz violating parameter is associated with the bumblebee gravity model. We study the motion of a particle in this bumblebee background where the dynamical variables satisfy non-canonical Snyder algebra along with some critical survey on the classical observations in the bumblebee background to see how these would likely differ from Schwarzschild background. It has been found that the perihelion shift acquires a generalized expression with two independent parameters. One of these two is connected with the Lorentz violating factor and the other is involved in the Snyder algeb…
Simpson-Visser regularization of the quantum Oppenheimer-Snyder-Datt black hole
该研究将 Simpson-Visser 正则化应用于量子 Oppenheimer-Snyder-Datt 黑洞，系统分析了其几何、轨道、热力学及准正则模，揭示了参数对观测量的不同约束作用及拓扑荷的改变。
We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover…
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