Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for extended bodies in general relativity.     

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.     

微粗糙面上方球形粒子的光散射及其散射截面的计算

基于互易定理研究了光波入射时微粗糙面与其上方球形粒子复合模型的光散射。根据粗糙表面电流积分方程并利用表面微扰展开，得到了微粗糙面表面极化电流的迭代解，给出了耦合电场的计算方法。结合散射耦合场散射矩阵和已有的微粗糙面及球形粒子的散射矩阵，给出了复合模型散射截面的计算公式，数值计算了复合模型的后向散射截面并进行了详细讨论。     

Behavior of a charged particle in a schwarzschild field

The influence of the De Witt self-action force on the motion of and electromagnetic emission from a charged particle in a Schwarzschild field is considered. It is shown that a charged particle in a Schwarzschild field is equivalent to a neutral particle of the same mass in a certain Reissner-Nordstrom field. A relationship is found between the power of the electromagnetic emission from an accelerated charge and the power of the thermal emission generated in a reference frame with the same acceleration at the event horizon. The quantum-mechanical problem of the motion of and emission from a charge in the field of a minihole is considered. Wave functions, the energy spectrum, and the widths of quasi-stationary levels are found with allowance for the De Witt self-action force. It is shown that the latter is important for large charges, when the solution becomes oscillatory. "Brainstorm" Little Science and Technology Enterprise. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 75–82, July, 1998.     

Gyroscopic precession in non-circular orbits: a phase-locked tetrad approach

We deduce the explicit form of a phase-locked (PL) tetrad, adapted to a small spinning particle (a test gyroscope) following an arbitrary geodesic orbit in the Schwarzschild geometry of a gravitational source. We subsequently obtain the analytic expression of the gyroscopic precessional velocity Ω in a non-circular orbit, by means of the Fermi rotation coefficients related to the tetrad’s transport law. As an application, we compute the orbital shift in the spin vector, considering a spinning test particle (the gyroscope) in a slightly non-circular orbital motion in the weak gravitational field limit. We compare our results with those of other previous works.     

Scattering of a Klein-Gordon particle by a black hole

By using the curved space-time Klein-Gordon equation, the form of the wave function of a scalar particle near a nonrotating black hole is obtained. It is shown that although the radial wave function oscillates infinitely rapidly near the black hole, the probability density remains finite even on the event horizon. This is consistent with the fact that the Schwarzschild surface is nonsingular. An expression is given for the large angular momentum scattering differential cross section by comparing the asymptotic form of the radial wave equation with the corresponding Coulomb radial wave equation in ordinary quantum mechanics.     

Tunneling of massive particles from noncommutative inspired Schwarzschild black hole

We apply the generalization of the Parikh–Wilczek method to the tunneling of massive particles from noncommutative inspired Schwarzschild black holes. By deriving the equation of radial motion of the tunneling particle directly, we calculate the emission rate which is shown to be dependent on the noncommutative parameter besides the energy and mass of the tunneling particle. After equating the emission rate to the Boltzmann factor, we obtain the modified Hawking temperature which relates to the noncommutativity and recovers the standard Hawking temperature in the commutative limit. We also discuss the entropy of the noncommutative inspired Schwarzschild black hole and its difference after and before a massive particle’s emission.     

Stability of general relativistic static thick disks: the isotropic Schwarzschild thick disk

We study the stability of general relativistic static thick disks. As an application we consider the thick disk generated by applying the “displace, cut, fill and reflect” method, usually known as the image method, to the Schwarzschild metric in isotropic coordinates. The isotropic Schwarzschild thick disk obtained from this method is the simplest model to describe, in the context of General Relativity, real thick galaxies. Stability under a general first order perturbation of the disk energy momentum tensor is investigated. The first order perturbation, when applied to the conservation equations, leads to a set of differential equations that have fewer equations than unknowns. In this article we search for perturbations in which the perturbation of the four velocity in a certain direction leads to a pressure perturbation in the same direction. We found that, in general, the isotropic Schwarzschild thick disk is stable under these kinds of perturbations.     

Point massive particle in General Relativity

It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein’s equations with $\delta $ δ -type source corresponding to a point particle is not known. In the present paper, we prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric solution of Einstein’s equations with $\delta $ δ -type energy-momentum tensor corresponding to a point particle. Solution of Einstein’s equations is understood in the generalized sense after integration with a test function. Metric components are locally integrable functions for which nonlinear Einstein’s equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighborhood.     

Average scattered field from a random PEC cylinder buried below a slightly rough surface

Scattering from a perfect electric conducting cylinder with random radius buried below a half space dielectric homogenous interface is studied. The cylindrical wave scattered by cylinder is expanded in terms of plane wave spectrum. Small perturbation method is used to study the interaction of each plane wave with the interface. The zeroth order term yields solution for a flat interface, whereas scattering from a rough surface is given by first-order term. Results are obtained for both TM and TE polarizations. Analytical expressions of the average scattered field are obtained and verified using numerical evaluation. Different scattering scenarios are simulated by varying the distribution of the radius. It is observed that average scattering cross section of an ensemble with normal/uniform distribution is almost equal to that of a cylinder with mean radius.     

Classical and quantum scattering by a gravitational center

The corrections to the leading term of the small-angle deflection of a classical particle by the Schwarzschild field and its linear approximation were found. The corresponding cross sections were obtained. The comparison with known in Born approximation cross sections for quantum massless particles of spins 0, 1, and 2 shows that only the leading term in all cases is the same. As the conditions for classical treatment are well fulfilled, this means that the classical results are much more accurate than the quantum one in Born approximation. The fact that the photon cross section is always smaller than that of massless scalar particle (both in Born approximation) suggests that with small probability (at least of order of the difference of these cross sections) the photon can fly by the Sun without deflection. The deflection of light, observable at a final distance from the Sun, is also considered and it is shown that measurements at the distances of several Sun’s radii will decide which coordinate system is the privileged one.     

Resonant scattering of light in a near-black-hole metric

We show that low-energy photon scattering from a body with radius R slightly larger than its Schwarzschild radius r _s resembles black-hole absorption. This absorption occurs via capture resulting in one of the many long-lived, densely packed resonances that populate the continuum. The lifetimes and density of these meta-stable states tend to infinity in the limit r _s →R. We determine the energy-averaged cross section for particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus a non-singular static metric may trap photons for arbitrarily long times, making it appear completely ‘black’ before the actual formation of a black hole.     

二维导体微粗糙面与其上方金属平板的复合电磁散射研究

研究了二维导体微粗糙面与其上方金属平板复合电磁散射特征.应用互易性原理使求解二次散射场简化为求解包含平板上的极化电流和微粗糙面散射场的积分方程，从而降低了求解难度.应用物理光学近似和微扰法分别求解了平板上的极化电流和粗糙面的电磁散射场，得到了复合散射截面计算公式并进行了数值计算.尤其对该复合模型后向耦合电磁散射结果进行了详细分析和讨论. 关键词： 互易性原理 复合电磁散射 微粗糙面 平板     

Asymptotic quasinormal modes of scalar field in a gravity’s rainbow

In the framework of the gravity's rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically calculated the asymptotic quasinormal frequencies, which depend on not only the mass parameter of the black hole, but also the particle's energy of the perturbation field. Meanwhile, the real parts of the asymptotic quasinormal modes can be expressed as T_H\ln 3, which is consistent with Hod's conjecture. In addition, for the quantum corrected black hole, the area spacing is independent of the particle's energy, even though the area itself depends on the particle's energy. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.     

A Model Detector for Hawking Radiation from a Schwarzschild Black Hole

A model detector for field quanta is considered from the point of view of a quantum field theory defined in asymptotically stationary regions of the Kruskal manifold and from that of a theory restricted to a Schwarzschild coordinate patch. A spherical array of oscillators at a constant distance r from the black hole, harmonic with respect to their proper time, is coupled to spherically symmetric Schwarzschild-modes of the field. The system is quantized and the energy expectation value of the coupled harmonic oscillators in a state of the field representing Hawking radiation is calculated. The back-reaction to the field may be interpreted in two controversial ways: In terms of the quantum field theory restricted to Schwarzschild space-time there is merely some scattering of the Hawking radiation, whereas in the framework of Kruskal quantum field theory particle production occurs.     

High-Speed Scattering of Charged and Uncharged Particles in General Relativity

After a brief consideration of the high-speed scattering of two point charges we thoroughly discuss high-speed scattering for a charged particle by a fixed mass and of two uncharged particles of comparable masses. We use perturbation technique over Minkowski spacetime in the de Donder gauge and solve the field equations and the resulting equations of motion (which take the reaction of the particles' quasistatic self-field into account) by iteration. The obtained energy-momentum conservation laws allow the computation of second-order corrections for the scattering angle and the cross section. The asymptotic structure of the far-field indicates synchrotron radiation (electromagnetic and gravitational, respectively) which causes an energy loss whose reaction on the motion is briefly considered in the low-velocity limit including bound motion. (For neutral particles this is a third-order effect).     

Relativistic electron scattering from freely movable proton/μ~+ in the presence of strong laser field

We have investigated the electron scattering from the freely movable spin-1/2 particle in the presence of a linearly polarized laser field in the first Born approximation.The laser-dressed state of electrons is described by a time-dependent wave function which is derived from a perturbation treatment.With the aids of numerical simulations, we explore the dependencies of the differential cross section on the laser field intensity as well as the electron-impact energy.Due to the mobility of the target, the differential cross section of this process is smaller than that of Mott scattering.     

Mass shift and width broadening of ρ-mesons produced in heavy ion collisions

The mass shift Δm_ρ and width broadening ΔΓ_ρ of ρ-mesons produced in heavy ion collisions is estimated using general formulae which relate the in-medium mass shift of a particle to the real part of the forward scattering amplitude Re f(E) of this particle on constituents of the medium and ΔΓ to the corresponding cross section. It is found that the mass increases by some tens of MeV but, more importantly, the width becomes large, increasing by several hundred MeV at beam energies of a few GeV·A and by twice that amount at beam energies of about a hundred GeV·A. Received: 28 July 1998     

An analytic perturbation approach for classical spinning particle dynamics

A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson–Papapetrou–Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle’s spin magnitude, it is shown how to obtain in general form an analytic representation of the particle’s kinematic and dynamical degrees of freedom that is formally applicable to infinite order in the expansion. Within this formalism, it is possible to identify a classical analogue of radiative corrections to the particle’s mass and spin due to spin–gravity interaction. The robustness of this approach is demonstrated by showing how to explicitly compute the first-order momentum and spin tensor components for arbitrary particle motion in a general space–time background. Potentially interesting applications based on this perturbation approach are outlined.     

Elastic scattering amplitude of a scalar particle in a plane wave field

The elastic scattering amplitude of a scalar particle in an arbitrary plane wave electromagnetic field is obtained in the form of a double integral by the method of dispersion relations. Particular cases of giving the plane wave field are investigated. It is shown that the existence of scalar particle radiation in an arbitrary plane wave electromagnetic field results in elastic scattering, whose amplitude determines the change in particle mass in this field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 32–37, May, 1990.