Hawking radiation as tunneling with back-reaction for the Kerr-anti-de Sitter black hole

Medved and Vagenas demonstrated how the Angheben-Nadalini-Vanzo-Zerbini analysis can be adapted in describing the effects of the gravitational back-reaction for the generic spherically symmetric black hole. We extend the Medved-Vagenas quantum tunneling method to the case of the stationary axisymmetric Kerr black hole in anti-de Sitter space-times. We find a correction to the Hawking radiation by considering the effects of the gravitational back-reaction and also energy conservation and angular momentum conservation.     

A Possibility for Studying Gravitational Properties of the Neutrino

We consider the effect that the gravitational field of a neutrino pulse radiated in the collapse of presupernova nuclei has on the observable optical radiation spectra of atoms at the supernova surface. We show that at the modern level of development of experimental methods, neutrino monitoring supplemented by optical monitoring of supernova candidates provides a unique possibility to check whether the Einstein equivalence principle is satisfied for neutrinos of each of the three types (electron, muon, and tau-lepton) and their antiparticles, to estimate the change of the gravitational potential at the surface of the star at the instant of the neutrino radiation pulse, and to obtain upper limits on the mass values of these neutrinos in a new way.     

Shell dynamics in the presence of a central body

We construct an idealized spherically symmetric relativistic model of an exploding object in the framework of the theory of surface layers in general relativity and match a Vaidya solution for a radially radiating star to another Vaidya solution through a thin spherical shell. We reduce the equations of motion and the radiation density of the Vaidya solution given by the matching conditions to a first-order system and analyze the general characteristics of the motion. We use a post-Newtonian approximation to find the equation of motion of a spherically symmetric radiating shell moving in a central gravitational potential.     

A proof of Price’s law for the collapse of a self-gravitating scalar field

A well-known open problem in general relativity, dating back to 1972, has been to prove Price’s law for an appropriate model of gravitational collapse. This law postulates inverse-power decay rates for the gravitational radiation flux through the event horizon and null infinity with respect to appropriately normalized advanced and retarded time coordinates. It is intimately related both to astrophysical observations of black holes and to the fate of observers who dare cross the event horizon. In this paper, we prove a well-defined (upper bound) formulation of Price’s law for the collapse of a self-gravitating scalar field with spherically symmetric initial data. We also allow the presence of an additional gravitationally coupled Maxwell field. Our results are obtained by a new mathematical technique for understanding the long-time behavior of large data solutions to the resulting coupled non-linear hyperbolic system of p.d.e.’s in 2 independent variables. The technique is based on the interaction of the conformal geometry, the celebrated red-shift effect, and local energy conservation; we feel it may be relevant for the problem of non-linear stability of the Kerr solution. When combined with previous work of the first author concerning the internal structure of charged black holes, which had assumed the validity of Price’s law, our results can be applied to the strong cosmic censorship conjecture for the Einstein-Maxwell-real scalar field system with complete spacelike asymptotically flat spherically symmetric initial data. Under Christodoulou’s C⁰-formulation, the conjecture is proven to be false.     

Impossibility of gravitational collapse

In the framework of the relativistic theory of gravity, we show that a universal mechanism for stopping the process of gravitational compression of a body with large mass with its subsequent radial expansion appears because of the gravitational field tensor. This excludes the gravitational collapse and the possibility of black hole formation.     

On the relation between ADM and Bondi energymomentaⅢ-perturbed radiative spatial infinity

In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D),we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity.The perturbation is given by defining the"real"time as the sum of the retarded time,the Euclidean distance and certain function f.     

On the relation between ADM and Bondi energy-momenta Ⅲ-perturbed radiative spatial infinity

In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbation is given by defining the "real" time as the sum of the retarded time, the Euclidean distance and certain function f.     

Similarity solution for a spherical shock wave in a non‐ideal gas under the influence of gravitational field and monochromatic radiation with increasing energy

The propagation of a spherical shock wave in a non‐ideal gas with or without gravitational effects is investigated under the action of monochromatic radiation. Similarity solutions are obtained for adiabatic flow between the shock and the piston. The numerical solutions are obtained using the Runge‐Kutta method of the fourth order. The density of the gas is assumed to be constant. The total energy of the shock wave is non‐constant and varies with time. The effects of change in values of non‐idealness parameter, gravitational parameter, shock Mach number, radiation parameter, and adiabatic exponent of the gas on shock strength and flow variables are worked out in detail. It is investigated that the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. A comparison is also made between the solutions in the cases of the gravitating and the non‐gravitating media. It is manifested that the gravitational parameter and the radiation parameter have in general opposite behaviour on the flow variables and the shock strength.     

导出匹配问题的NP-完全性以及导出匹配可扩问题的CO-NP-完全性

图Ｇ的一个匹配Ｍ是导出的,若Ｍ是图Ｇ的一个导出子图。图Ｇ是导邮匹配可扩的（简记ＩＭ－可扩的）,若图Ｇ的任一导出匹配均含于图Ｇ的一个完美匹配当中。本文我们将证明如下结果。⑴对无爪图而言,问题“给定图Ｇ以及一个正整数ｒ,确定是否存在图Ｇ的一个导出匹配Ｍ使得Ｍ≥ｒ”是ＮＰ－完全的。⑵对直径为２的图以及直径为３的偶图,问题“确定一个给定图是否为导出匹配可扩的”是ＣＯ－ＮＰ完全的;而对完全多部图而言,问题“     

Unique Maximum Matching Algorithms

We consider the problem of testing the uniqueness of maximum matchings, both in the unweighted and in the weighted case. For the unweighted case, we have two results. First, given a graph with n vertices and m edges, we can test whether the graph has a unique perfect matching, and find it if it exists, in O(m log⁴ n) time. This algorithm uses a recent dynamic connectivity algorithm and an old result of Kotzig characterizing unique perfect matchings in terms of bridges. For the special case of planar graphs, we improve the algorithm to run in O(n log n) time. Second, given one perfect matching, we can test for the existence of another in linear time. This algorithm is a modification of Edmonds' blossom-shrinking algorithm implemented using depth-first search. A generalization of Kotzig's theorem proved by Jackson and Whitty allows us to give a modification of the first algorithm that tests whether a given graph has a unique f-factor, and find it if it exists. We also show how to modify the second algorithm to check whether a given f-factor is unique. Both extensions have the same time bounds as their perfect matching counterparts. For the weighted case, we can test in linear time whether a maximum-weight matching is unique, given the output from Edmonds' algorithm for computing such a matching. The method is an extension of our algorithm for the unweighted case.     

New mechanism of energy release in astrophysical objects

Conclusions The above qualitative analysis of the evolution of astrophysical objects shows that in the field theory of gravitation with minimal coupling objects in the regionM/a<1/3 of values of the mean gravitational potential are stable to small perturbations of their radius with unchanged rest mass.However, the mean gravitational potential of these objects increases when they capture matter surrounding them. When the mean potential reaches the valueM/a=1/3, the object passes abruptly from an infinitely stable state to an infinitely unstable state (with respect to small perturbations of its radius). Therefore, even small perturbations in the radius of the object once the critical value of the mean gravitational potential has been reached necessarily lead to expansion of the matter, which may be accompanied by the ejection of mass of this object and the release of energy.Therefore, instead of gravitational collapse, the outcome of the instability of astrophysical objects in general relativity, in the present theory there is a new mechanism of energy release.Scientific-Research Institute of Nuclear Physics at the Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 48, No. 3, pp. 275–283, September, 1981.     

Collapse and Rebound of a Gas Bubble

In this paper, we study the collapse and rebound of a gas bubble. Our goals are twofold: (1) we want to stress that different mathematical models may lead to extremely different results and (2) we introduce a new class of simplified reliable models. We accomplish our first goal by showing that the results obtained from two of the simplest and most widely used models (the isothermal and adiabatic approximations) are very different while the bubble is highly compressed. This period of time is short but it is of crucial importance in most phenomena where bubble collapses are relevant. To accomplish our second goal, we identify a nondimensional parameter that is a quantification of the strength of the bubble collapse and we show how to use this large parameter to obtain new simplified models through the use of standard asymptotic techniques. Illustrative examples and discussions on the wide range of applicability of the approach introduced in this work are given.     

Nonlinear shear‐free radiative collapse

We study realistic models of relativistic radiating stars undergoing gravitational collapse which have vanishing Weyl tensor components. Previous investigations are generalized by retaining the inherent nonlinearity at the boundary. We transform the boundary condition to an Abel equation of the first kind. A variety of nonlinear solutions is generated all of which can be written explicitly. Several classes of infinite solutions exist. Copyright © 2007 John Wiley & Sons, Ltd.     

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev–Petviashvili (KP) approximation, Green–Naghdi equations, Serre approximation and full-dispersion model. We first introduce a “variable” nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.     

Renormalized two-body low-energy scattering

For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension d ≥ 3, we introduce a stationary scattering theory for Schrödinger operators which is regular at zero energy. In particular, it is well-defined at this energy, and we use it to establish a characterization there of the set of generalized eigenfunctions in an appropriately adapted Besov space, generalizing parts of [DS1]. Principal tools include global solutions of the eikonal equation and strong radiation condition bounds.     

La radiation Hawking à l’horizon d’un trou noir

We establish the polarization of the quantum vacuum to a thermal state with the Hawking temperature, at the future black-hole horizon created by a gravitational collapse.     

Hill regions of charged three-body systems

For charged three-body systems, we discuss the configurations and orientations that are admissible for given values of the conserved total energy and angular momentum. The admissible configurations and orientations are discussed on a configuration space that is reduced by the translational, rotational and dilation symmetries of charged three-body systems. We consider the examples of the charged three-body systems given by the helium atom (two electrons and a nucleus) and the compound of two electrons and one positron. For comparison, the well known example of the Newtonian gravitational three-body system is discussed for the scheme presented in this paper first.     

The stress-energy tensor of matter as a gravitational field source

This article discusses the hypothesis that the universally conserved stress-energy tensor of matter is the source of the gravitational field. From this hypothesis, it immediately follows that space-time must be Riemannian. In contrast to the general theory of relativity, in the gravitational theory based on this hypothesis, the concept of an inertial coordinate system, acceleration relative to space, and the laws of conservation of the energy and angular momenta are retained. In the framework of this theory, the gravitational field is a physical field. The theory explains all observable facts of the solar system, predicts the existence of a large hidden mass of matter in a homogeneous and isotropic universe, and assumes that such a universe can only be “flat.” The theory changes the established idea of the collapse of large massive bodies. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 5–24, January, 1997.