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 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.
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
School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学学院）；School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）
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
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）；Department of Physics, Shanghai University（上海大学物理系）
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…
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.
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…
Quantum Oppenheimer-Snyder black hole evaporation and its fate
School of Science, Hunan Institute of Technology（湖南工学院理学院）；School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学科学学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
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
The Assam Royal Global University（阿萨姆皇家全球大学）；Secretaria da Educação do Ceará (SEDUC), Coordenadoria Regional de Desenvolvimento da Educação (CREDE 9)（塞阿拉州教育厅（SEDUC），区域教育发展协调局（CREDE 9））；Echahid Cheikh Larbi Tebessi University（谢赫·拉里比·特贝西烈士大学）；Khazar University（哈扎尔大学）
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…
Josephson interferometry in an Oppenheimer--Snyder-like scale-dependent black-hole spacetime
Eastern Mediterranean University（东地中海大学）；Mapúa University（马普阿大学）；Università degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）
Naked Singularities and Black Hole Thermodynamics from Shadows and Photon Rings in the Quantum Oppenheimer-Snyder Model
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Fesenkov Astrophysical Institute（费森可夫天体物理研究所）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Università di Roma “La Sapienza”（罗马第一大学）
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…
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…
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
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Fesenkov Astrophysical Institute（费森科夫天体物理研究所）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马第一大学物理系与ICRA中心）
Oppenheimer-Snyder Collapse in f(R) Gravity : Stalemate or Resolution?
Vellore Institute of Technology（维洛尔理工学院）；Inter-University Centre for Astronomy and Astrophysics (IUCAA)（大学间天体物理中心）；Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学）
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
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Fesenkov Astrophysical Institute（费森可夫天体物理研究所）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马大学“智慧大学”物理系及ICRA中心）
Classification of Oppenheimer-Snyder Collapse: Singular, Bouncing, and Soft-Landing Scenarios
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University（天津大学国际联合研究院）
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…
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…
Joint Constraints on Quantum Oppenheimer--Snyder Black Holes from High-Frequency Quasi-Periodic Oscillations in X-ray Binary Systems and the S2 Star Orbit
University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；Khazar University（哈扎尔大学）；Jadara University（贾达拉大学）；Hassan II University of Casablanca（卡萨布兰卡哈桑二世大学）；Ibn Tofail University（伊本·图菲利大学）；Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆理论物理国际中心）；Central Asian University（中亚大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Ulugh Beg Astronomical Institute（乌鲁格别克天文研究所）；Kimyo International University in Tashkent（塔什干化学国际大学）
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…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4 dimensional spacetime manifold. Using a semi-tetrad covariant formalism, that provides a set of geometrical and matter variables, we transparently demonstrate the evolution of the trapped region and also extend Hawking's topology theorem to a wider class of spacetimes. In addition, we perform a stability analysis for the apparent horizons in this formalism,…
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…
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…
