We explore in detail the semiclassical environment of collapsing shells of matter, and determine the semiclassical flux measured by a variety of observers. This study is a preliminary step in a broader investigation of thermodynamic properties of the geometry of collapsing objects. Specifically, in this paper we consider spherically symmetric null and timelike collapsing shells which form an event horizon, and calculate the flux measured by observers both inside and outside the shell, and both inside and outside the event horizon, and find nontrivial results in most of the cases. Additionally, we also investigate the environment of a shell which collapses but \emph{does not} form a horizon, halting at some radius larger than the Schwarzschild radius, and find that such an object generically gives rise to a pulse of radiation which is sharply peaked as it travels inwards and is reflected at the origin, and eventually emerges from the shell in a "thermalized" form. Our results have potential consequences in addressing questions pertaining, e.g. to black hole entropy and backreaction.
We consider a collapsing shell of matter to form the Hayward black hole and investigate semiclassically quantum radiation from the shell. Using the Israel's formulation, we obtain the mass relation between the collapsing shell and the Hayward black hole. By using the functional Schrödinger formulation for the massless quantum radiation, the evolution of a vacuum state for a scalar field is shown to be unitary. We find that the number of quanta at a low frequency decreases for a large length parameter characterizing the Hayward black hole. Moreover, in the limit of low frequency, the Hawking te…
Radiation from collapsing shells, semiclassical backreaction and black hole formation
本文详细分析了坍缩壳层周围的量子场论，并讨论了与辐射通量发射和黑洞形成有关的几个概念性问题。显式计算使用模型的崩溃壳，原来是解析可解的。我们使用在这个模型中获得的见解，得出可靠的结论，更现实的模型。我们首先表明，任何壳质量$M$塌缩到一个半径接近$r=2M$将发出近似热辐射的一段时间。特别是，一个壳层从某个初始半径坍缩到最终半径$2M(1-ε^2)^{-1}$（其中$ε\ll 1$）而不形成黑洞，它将在周期$M\lesssim t \lesssim M\ln (1/ε^2)$期间发射热辐射。稍后（$t\gg M \ln(1/ε^2)$），来自这样一个壳层的通量将按指数衰减到零。接下来，我们研究使用应力张量的真空期望值计算的反作用对坍缩的影响。我们发现，在任何现实的坍缩场景中，逆反应效应的\emph{not}阻止事件视界的形成。事件视界形成的时间，当然，由于辐射通量的原因而延迟--辐射通量减少了壳层的质量--但这种效应不足以阻止视界的形成。我们还澄清了几个概念问题，并在论文的附录中提供了计算的教学细节。
The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. The encountered properties are investigated making use of the Israel junction conditions on the shell, considering that it is the boundary between two spherically symmetric spacetimes. Using this method, and considering two different Kantowski-Sachs spacetimes as a representation for the Schwarzschild spacetime, the relevant quantities on the shell are computed, such as its stress-energy tensor and the action for the whole spacetime. From the …
In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schrödinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schrödinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and…
We study radiation emitted during the gravitational collapse from two different types of shells. We assume that one shell is made of dark matter and is completely transparent to the test scalar (for simplicity) field which belongs to the standard model, while the other shell is made of the standard model particles and is totally reflecting to the scalar field. These two shells have exactly the same mass, charge and angular momentum (though we set the charge and angular momentum to zero), and therefore follow the same geodesic trajectory. However, we demonstrate that they radiate away different…
We present results of a comprehensive study of collapsing and bouncing thin shells with rotation, framing it in the context of the weak cosmic censorship conjecture. The analysis is based on a formalism developed specifically for higher odd dimensions that is able to describe the dynamics of collapsing rotating shells exactly. We analise and classify a plethora of shell trajectories in asymptotically flat spacetimes. The parameters varied include the shell's mass and angular momentum, its radial velocity at infinity, the (linear) equation-of-state parameter and the spacetime dimensionality. We…
We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding, at the moment their radii are equal, and find a probability that the system is a black hole which is in qualitative agreement with what one would expect according to the hoop conjecture and the uncertainty principle of quantum physics, and parallels the results obtained for simpler sources. One new feature however emerges, in that this probability shows a m…
We investigate gravitational collapse of a spherically symmetric thin shell in the Einstein-Gauss-Bonnet (EGB) gravity. Under the recently proposed 4D limit, we find that the collapsing shell will be bounced back at a small radius, without forming a singularity. This bouncing behavior is similar to those of a test particle and a homogeneous spherical dust star, in accordance with the expectation that the Gauss-Bonnet term will modify the small scale behavior of the Einstein gravity. We analyze the causal structure of the dynamic spacetime that represents the bouncing process, finding that the …
Galileon radiation in the collapse of a thin spherical shell of matter is analyzed. In the framework of a cubic Galileon theory, we compute the field profile produced at large distances by a short collapse, finding that the radiated field has two peaks traveling ahead of light fronts. The total energy radiated during the collapse follows a power law scaling with the shell's physical width and results from two competing effects: a Vainshtein suppression of the emission and an enhancement due to the thinness of the shell.
We study the gravitational collapse of two thin shells of matter, in asymptotically flat spacetime or constrained to move within a spherical box. We show that this simple two-body system has surprisingly rich dynamics, which includes prompt collapse to a black hole, perpetually oscillating solutions or black hole formation at arbitrarily large times. Collapse is induced by shell crossing and the black hole mass depends sensitively on the number of shell crossings. At certain critical points, the black hole mass exhibits critical behavior, determined by the change in parity (even or odd) of the…
Hawking radiation explicitly depends only on the black hole's total mass, charge and angular momentum. It is therefore generally believed that one cannot reconstruct the information about the initial mass distribution of an object that made the black hole. However, instead of looking at radiation from a static black hole, we can study the whole time-dependent process of the gravitational collapse, and pre-Hawking radiation which is excited because of the time-dependent metric. We compare radiation emitted by a single collapsing shell with that emitted by two concentric shells of the equivalent…
We investigate the fate of the classical singularity in a collapsing dust cloud. For this purpose, we quantize the marginally bound Lemaitre-Tolman-Bondi model for spherically-symmetric dust collapse by considering each dust shell in the cloud individually, taking the outermost shell as a representative. Because the dust naturally provides a preferred notion of time, we can construct a quantum mechanical model for this shell and demand unitary evolution for wave packets. It turns out that the classical singularity can generically be avoided provided the quantization ambiguities fulfill some we…
We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in…
The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quan…
We study the motion of thin-shell bubbles and their tunneling in anti de Sitter (AdS) background. We are interested in the case when the outside of a shell is a Schwarzschild-AdS space (false vacuum) and the inside of it is an AdS space with a lower vacuum energy (true vacuum). If a collapsing true vacuum bubble is created, classically it will form a Schwarzschild-AdS black hole. However, this collapsing bubble can tunnel to a bouncing bubble that moves out to spatial infinity. Then, although the classical causal structure of a collapsing true vacuum bubble has the singularity and the event ho…
We study the harvesting of correlations by two Unruh-DeWitt static detectors from the vacuum state of a massless scalar field in a background Vaidya spacetime consisting of a collapsing null shell that forms a Schwarzschild black hole (hereafter Vaidya spacetime for brevity), and we compare the results with those associated with the three preferred vacua (Boulware, Unruh, Hartle-Hawking-Israel vacua) of the eternal Schwarzschild black hole spacetime. To do this we make use of the explicit Wightman functions for a massless scalar field available in (1+1)-dimensional models of the collapsing spa…
We study the quantum effects of a test Klein-Gordon field in a Vaidya spacetime consisting of a collapsing null shell that forms a Schwazschild black hole, by explicitly obtaining, in a $(1+1)$-dimensional model, the Wightman function, the renormalised stress-energy tensor, and by analysing particle detector rates along stationary orbits in the exterior black hole region, and make a comparison with the folklore that the Unruh state is the state that emerges from black hole formation. In the causal future of the shell, we find a negative ingoing flux at the horizon that agrees precisely with th…
We study Hawking radiation on the quantum spacetime generated by a quantum ingoing null shell in the 2d theory proposed by Callan-Giddings-Harvey-Strominger (CGHS). The quantum spacetime is a superposition of classical geometries with uncertainty in position and momentum of the collapsing shell. The Hawking radiation spectrum is computed, revealing a non-thermal behavior for finite time as well as a dependence on the shell's physical degrees of freedom. Hawking radiation's dependence on the collapsing shell becomes irrelevant in the late time approximation as we reach $i^+$ since the radiation…
Inhomogeneous dust collapse in five-dimensional AdS-Chern-Simons gravity
Facultad de Ciencias, Universidad Arturo Prat（阿图罗·普拉特大学理学院）；Instituto de Ciencias Exactas y Naturales (ICEN), Universidad Arturo Prat（阿图罗·普拉特大学精确与自然科学研究所）；Departamento de Ciencias Exactas, Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院精确科学系）
We propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(-B), where B is the Bekenstein-Hawking entropy of the intermediate b…
We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking's original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when q…
In case of spherical symmetry, the assumptions of finite-time formation of a trapped region and regularity of its boundary --- the apparent horizon --- are sufficient to identify the form of the metric and energy-momentum tensor in its vicinity. By comparison with the known results for quasistatic evaporation of black holes, we complete the identification of their parameters. Consistency of the Einstein equations allows only two possible types of higher-order terms in the energy-momentum tensor. By using its local conservation, we provide a method of calculation of the higher-order terms, expl…
We provide a quantum picture for the emergence of a bouncing cosmology, according to the idea that a semiclassical behavior of the Universe towards the singularity is not available in many relevant Minisuperspace models. In particular, we study the Bianchi I model in vacuum adopting the isotropic Misner variable as an internal clock for the quantum evolution. The isomorphism between the Wheeler-DeWitt equation in this Minisuperspace representation and the Klein-Gordon one for a relativistic scalar field allows to identify the positive and negative frequency solutions as associated to the colla…
Black hole radiation from an infinitesimally thin massive collapsing shell, possessing a global monopole charge, which in turn leads to a Schwarzschild black hole with a global monopole charge has been shown to be processed by a unitary evolution. The exterior metric of the collapsing shell is described by the global monopole (GM) metric. The analysis is performed using the Wheeler-deWitt formalism which gave rise to a Schrödinger-like wave equation. Existence of unitarity is confirmed from two independent lines of approach. Firstly, by showing that the trace of the square of the density matri…
