Exact relativistic models of conformastatic charged dust thick disks

We construct relativistic models of charged dust thick disks for a particular conformastatic spacetime through a Miyamoto–Nagai transformation used in Newtonian gravity to model disk like galaxies. Two simple families of thick disk models and a family of thick annular disks based on the field of an extreme Reissner–Nordström black hole and a Morgan–Morgan-like metric are considered. The electrogeodesic motion of test particles around the structures are analyzed. Also the stability of the particles against radial perturbation is studied using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models built satisfy all the energy conditions.     

Stability of general relativistic gaseous masses and variational principles

The Einstein field equations for a self-gravitating fluid that obeys an equation of state of the formp=p(w),p the pressure andw the energy density may be derived from a variational principle. The perturbations of the metric tensor and the fluid dynamic variables satisfy equations which may be derived from a related variational principle, namely the principle associated with the second variation problem. It is shown that the variational principle given by Chandrasekhar from which a sufficient criterion may be obtained for deciding when a self gravitating spherical gaseous mass is unstable against spherically symmetric perturbations is that given by the second variation problem. It is further shown that this criterion is equivalent to requiring that the integral entering into the second variation be negative. The latter form of the criterion may be used in general situations.This work was supported in part by the United States Atomic Energy Commission under contract number AT (11-1)-34, Project Agreement Number 125.     

Resonant behavior of stochastic oscillations of general relativistic disks driven by a memory-damped friction

By using a generalized Langevin equation to describe the vertical oscillations of a general relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density(PSD) of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of the system parameters on the resonant behavior in PSD curves. The results show that as the damping strength α and memory time τ of the friction increase, the variation of PSD with spectrum frequency f from monotonous decreasing to occurring maximums, and the phenomenon of a general stochastic resonance(SR) with a single peak and multi-peaks can be found in PSD curves. The radial distance parameter n, the mass M, and spin parameter a* of the black hole determine the inherent frequency of vertical oscillations in the disk,and they have significant influences on the SR phenomena in a system of black hole binaries.     

On the twin paradox in static spacetimes: I. Schwarzschild metric

Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.     

Stability of Scalar Modified Schwarzschild Solution

It is shown that the Schwarzschild solution in general relativity, reconsidered adding to the vacuum a massless scalar field, is stable to perturbations from radiation fields of spin s = 0, ±1/2, ±1, ±2.     

厚圆盘弯曲振动研究

当厚跨比大于五分之一时,研究板弯曲振动中的剪切应力及由此引起的剪切、扭转变形等就不能忽略,经典的薄板理论将失效.从声学应用的角度,基于Mindlin板理论,本文推导了厚圆盘弯曲振动径向位移和横向位移的解析表达式,并得到了自由、简支、固定边界条件下的频率方程.解析方法计算得到的前几阶振型对应的频率与有限元方法计算的结果基本相符,与实验测试结果基本一致.本文的结果对厚圆盘弯曲振动辐射器的设计提供了理论参考. 关键词： 厚圆盘 弯曲振动 频率方程     

Stability of self-gravitating astrophysical disks

Criteria which guarantee the stability of self-gravitating gaseous and stellar disks toward any localized small perturbations are obtained. These criteria are formulated as inequalities of the form Q>Q _c (separately for gas and stars). The latter should be satisfied by the “stability parameter” Q, which is equal, by definition, to unity on the stability boundary of radial perturbations. The critical value of the stability parameter Q _c is appreciably greater than (although of the order of) unity, attesting to the great instability of nonaxially symmetric perturbations. It is shown that the stability criterion derived for gaseous disks is valid for disks rotating within a spheroidal component (as in spiral galaxies) or in the field of a central mass (planetary rings and accretion disks). Stellar disks are stabilized with significantly greater difficulty. This is attributable mainly to the anisotropy of the velocity distribution inherent to them, which is favorable for instability. Zh. éksp. Teor. Fiz. 112, 771–795 (September 1997)     

Rediscussion of the Stability Problem of the Schwarzschild Black Hole

We use the Kruskal time coordinate T to define the initial time. By this way, the stability study naturally becomes the one connected with the two regions, i.e. the white-hole-connected region and the black-hole-connected region. The union of the two regions covers the Schwarzschild space-time （r ≥ 2m）. We also obtain the very reasonable conclusion： the white-hole-connected region is unstable and the black-hole-connected region is stable. If we take the instability with caution and seriousness, it is not unreasonable to regard that the Schwarzschild black hole might be unstable to some extent.     

On the Backward Stability of the Schwarzschild Black Hole Singularity

We study the backwards-in-time stability of the Schwarzschild singularity from a dynamical PDE point of view. More precisely, considering a spacelike hypersurface \({\Sigma_0}\) in the interior of the black hole region, tangent to the singular hypersurface \({\{r = 0\}}\) at a single sphere, we study the problem of perturbing the Schwarzschild data on \({\Sigma_0}\) and solving the Einstein vacuum equations backwards in time. We obtain a local backwards well-posedness result for small perturbations lying in certain weighted Sobolev spaces. No symmetry assumptions are imposed. The perturbed spacetimes all have a singularity at a “collapsed” sphere on \({\Sigma_0}\), where the leading asymptotics of the curvature and the metric match those of their Schwarzschild counterparts to a suitably high order. As in the Schwarzschild backward evolution, the pinched initial hypersurface \({\Sigma_0}\) ‘opens up’ instantly, becoming a regular spacelike (cylindrical) hypersurface. This result thus yields classes of examples of non-symmetric vacuum spacetimes, evolving forward-in-time from regular initial data, which form a Schwarzschild type singularity at a collapsed sphere. We rely on a precise asymptotic analysis of the Schwarzschild geometry near the singularity which turns out to be at the threshold that our energy methods can handle.     

Electromagnetic radiation of relativistic electrons in thick crystals

Angular distributions of soft gamma quanta and spectra of electron radiation intensity are compared in diamond crystals of various thickness for axial orientation. Narrow directionality of the soft gamma quanta and a weak dependence of angular width of the distribution on crystal thickness are noted. For axial orientation the angular width of the soft gamma quantum distribution comprises ± 2_L for diamond, silicon, and tungsten crystals. Radiation losses into the collimator _c = 1/ for axial orientation increases with thickness and reach their maximum value at t 0.1 radiation length. It is shown experimentally that maximum values of radiation loss into the cone ^–1 can be achieved in crystals of the light-elements.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 32–38, September, 1986.     

Exact relativistic models of perfect fluid disks in a magnetic field

Using the well-known “displace, cut and reflect” method we construct thin disks made of a perfect fluid in presence of a magnetic field. The models are based in a magnetic Reissner-Nordstrom metric of Einstein-Maxwell equations for a conformastatic spacetime. The influence of the magnetic field on the matter properties of the disk are analyzed. We also study the motion of charged test particles around the disks. We construct models of perfect fluid disks satisfying all the energy conditions.     

Quantum dynamics of an isotropic cosmological model with relativistic gas

A canonical time parameter corresponding to the synchronous reference frame is found for an isotropic cosmological model with relativistic gas. Canonical quantization of the model is performed. In the quantum theory, the radius of the Universe is an operator-valued function of time, whose values at different moments of time commute among themselves, and the state of the Universe itself does not change with time. In particular, this means that in experiments in which the radius of the Universe is measured, the presence of singularity is unavoidable within a finite interval of time in the past, and, for closed models, in the future.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 9–14, July, 1990.The authors thank L. D. Faddeev for his interest to their work, and V. A. Franke for stimulating discussions.     

Quantum construction of general relativistic spacetime

A construction of a model of general relativistic spacetime that arises naturally from within standard quantum theory is presented. In terms of this model all the usual structures of general relativity theory can be given a quantum-theoretic interpretation, so that the usual barriers between the two theories are absent.     

Newtonian view of general relativistic stars

The angular ADM reduction of the BTZ spacetime yields a Liouville-type theory. The analysis of the resulting Liouville theory naturally leads to the identification of the stretched horizon. The dynamics associated with the stretched horizon has a feature that seems consistent with the unsmooth horizon; the quantum gravity effects are essential for the unsmoothness. We show that the “anomaly” term in the stress–energy tensor is responsible for the Planck scale energy experienced by an infalling observer.     

Efficiency of annular finite elements for flexural vibrations of thick disks

The efficiency is evaluated of various semianalytical annular finite elements in predicting the vibrational modes for disks where the effect of transverse shear and rotary inertia becomes important, with reference both to the minimum number of degrees of freedom and to the minimum number of operations required to achieve a certain approximation for the exact natural frequency value. From this point of view, a new element, in which normal displacements are interpolated by cubic polynomials and rotations by parabolic polynomials along the radius, is compared with other elements described in the literature.