Dynamics of a gravitational field. III

The paper investigates the dynamic characteristics of a system of confined sources with gravitational radiation. The gravitational forces acting on test particles, the energy density, the total energy of the system and the total flux of gravitational energy are calculated. These determinations are compared with those carried out previously in the investigations of other authors.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 47–54, August, 1973.     

Dynamics of a gravitational field. II

In the paper, the alternative proposed earlier for the dynamic theory of a gravitational field is compared with other well-known theories. An analysis is carried out of two exact solutions of Einstein's equations. The results coincide with those obtained earlier in other investigations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 40–47, August, 1973.In conclusion, we would take the opportunity to express our sincere thanks to V. I. Rodichev for support and valuable comments.     

Dynamics of a gravitational field. IV

The basis of the assumptions made for the construction of the dynamic theory of a gravitational field are presented in this paper. For this purpose, the results of recent investigations of different authors are included, devoted to the establishment of conformity between the dynamic field theories in two-dimensional space and the general theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 99–103, September, 1973.     

Dynamics of a vertical flight in the stationary gravitational field of a celestial body: Post-newtonian corrections and gravitational redshift

The standard problem of a radial motion of test particles in the stationary gravitational field of a spherically symmetric celestial body is solved and is used to determine the time features of this motion. The problem is solved for the equations of motion of general relativity (GR), and the time features are obtained in the post-Newtonian approximation, with linear GR corrections proportional to r _g /r and β ² (in the solution being considered, they are of the same order of smallness) being taken rigorously into account. Total times obtained by integrating the time differentials along the trajectories of motion are considered as the time features in question. It is shown that, for any parameters of the motion, the proper time (which corresponds to watches comoving with a test particle) exceeds the time of watches at rest (watches at the surface of the celestial body being considered). The mass and the radius of the celestial body, as well as the initial velocity of the test particle, serve as arbitrary parameters of the motion. The time difference indicated above implies a leading role of the gravitational redshift, which decreases somewhat because of the opposite effect of the Doppler shift. The results are estimated quantitatively for the important (from the experimental point of view) case of vertical flights of rockets starting from the Earth’s surface. In this case, the GR corrections, albeit being extremely small (a few microseconds for several hours of the flight), aremeasurable with atomic (quantum) watches.     

The static gravitational field near spatial infinity I

A static solution to Einstein's equations, which is asymptotically flat near spatial infinity, is shown to be asymptotically Schwarzschildian. As an application of this result we prove a technical lemma on the existence of asymptotically flat harmonic coordinates near infinity.     

Convection in a gravitational field

We set up a classical stochastic model for the irreversible dynamics of a lattice gas under gravity. We show that for a class of initial states the system converges to equilibrium, which obeys the laws of thermostatics.Dedicated to Oliver Penrose.     

Non-linear quark theory of a spin 2 field (gravitational mesons). I

An equation for a spin 2 meson octet (an octet of gravitational mesons) interacting with mesons of spin 0^– and 1^– is derived in the context of a non-linear quark model by the confluence method. We determine the magnetic moments and the decay constants for the octet of gravitational mesons into mesons of spin 0^– and 1^–.Translated from Izvestiya VUZ, Fizika, No. 3, pp. 94–100, March, 1973.     

The gravitational field of a nullicle

We present a natural generalization of the Schwarzschild solution. It is an exact solution of the vacuum Einstein field equations and is interpreted as the gravitational field of a nullicle (null-particle).     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Black hole in a gravitational field

An exact solution of the vacuum Einstein field equations representing a Schwarzschild black hole in an external gravitational field is derived using a formalism developed by Ernst.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Relativistic gas in a gravitational field

Equations describing the kinetics and hydrodynamics of a relativistic gas in a gravitational field are obtained using the concept of a gravitational field as a physical field in a pseudo-Euclidean space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1982.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Dynamics of a gravitational billiard with a hyperbolic lower boundary

Gravitational billiards provide a simple method for the illustration of the dynamics of Hamiltonian systems. Here we examine a new billiard system with two parameters, which exhibits, in two limiting cases, the behaviors of two previously studied one-parameter systems, namely the wedge and parabolic billiard. The billiard consists of a point mass moving in two dimensions under the influence of a constant gravitational field with a hyperbolic lower boundary. An iterative mapping between successive collisions with the lower boundary is derived analytically. The behavior of the system during transformation from the wedge to the parabola is investigated for a few specific cases. It is surprising that the nature of the transformation depends strongly on the parameter values. (c) 1999 American Institute of Physics.     

Hard thermal loops in a gravitational field

We calculate the high-temperature (T ⁴) limit of the 3-graviton vertex function, with a single loop of internal scalar particles in thermal equilibrium. We use the analytically continued imaginary-time formalism. We verify a particular case of the Ward identity connecting the 3- and 2-graviton functions. This confirms that there is covariance under general coordinate transformations (which reduce to the identity at infinity). We remark that the ghost-ghost-graviton vertex (with ghost and graviton internal lines) has noT ⁴ term. This implies that the 3-graviton function with internal graviton (and ghost) lines must satisfy the Ward identity too, so it is possible for it to be proportional to the scalar contribution. We have verified this for that part of the vertex function which is manifestly symmetric and traceless in the six Lorentz indices.     

Orbital equations in a weak gravitational field

With the obtainment of the Synge equations of motion in third approximation for a test particle, we determine the relativistic force in the field generated by a massive body obtained previously in terms of its potentials. Afterwards, in order to study the motion, we obtain the integral of energy and the integral of angular momentum. By means of them, the general form for the trajectory of an equatorial orbit and for the advance of its apsidal line are obtained. As we will see, the known diverse contributions for this advance appears in the general form after strong supplementary conditions on the potentials. As application, with such assumptions these contributions are derived in a unified way.     

Phase ordering dynamics in a gravitational field

We study the dynamics of phase ordering in the presence of an external gravitational field, namely a field that varies linearly with distance in one direction. Starting from microscopic considerations, we motivate reasonable phenomenological models for cases with nonconserved and conserved order parameter. We present detailed numerical results from our model for the case with conserved order parameter.     

Trapped Bose condensate in a gravitational field

The Bose condensation of atoms in finite 1D and 2D parabolic traps placed in a gravitational field is considered. The distortion of the trap potential in this field is modeled by a combination of two rectangular 1D and 2D traps. The change in the critical temperature T _c is found with regard to the cutoff and renormalization of the spectrum of these model potentials. The shift of the critical temperature T _c in the gravitational field is calculated. The shift sign and magnitude depend on the way of introducing the gravitational field. For a certain choice, three critical temperatures can be sequentially observed. These temperatures can be attributed to three Bose condensations that occur in the cyclic motion of the trap along the Earth (I)-space (II)-Earth (III) route.