Electrodynamics in the general theory of relativity 2. Properties of asymptotically planar spaces with electromagnetic radiation

The Newman-Penrose method is used to study the asymptotic behavior of spaces with finite sources and electromagnetic and gravitational radiation. Expansions are found for the Maxwell and Weyl tensors and for the metric in inverse powers of distance from the system of sources. The total energy of the system, including the energy of the gravitational and electromagnetic fields, is defined for a particular case.Translated from Izvestiya VUZ. Fizika, No. 3, pp. 7–14, March, 1970.     

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.     

Static Plane-Symmetric Nonlinear Spinor and Scalar Fields in GR

We consider a system of minimally coupled nonlinear spinor and scalar fields within the scope of a plane-symmetric gravitational field. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The change of the sign of the scalar field energy density of the system in question realizes physically if and only if the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. The choice of spinor field nonlinearity leads to the elimination of scalar field contribution to the metric functions, but leaves its contribution to the total energy unaltered. The spinor field is more sensitive to the gravitational field than the scalar field.     

The Gravitational Energy–Momentum Density of Radially Accelerated Observers in Schwarzschild Spacetime

A hybrid machinery that is useful for calculations in teleparallel theories when the spacetime is spherically symmetric is developed. Using this machinery, the gravitational energy–momentum tensor density of the Schwarzschild spacetime is evaluated in a frame adapted to observers that accelerate in the radial direction. The energy density, the total energy, and the gravitational energy-momentum flux are obtained. The regularization procedure and the limit where gravity is absent is discussed. It turns out that the regularized energy and energy–momentum flux are consistent in the whole spacetime. The continuity equation for the gravitational energy–momentum also holds for any point outside the black hole. Finally, the static and freely falling cases are discussed. It is found that a static observer measures a negative gravitational energy density, while a freely falling one measures a vanishing density.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

Binary Mixture of Perfect Fluid and Dark Energy in Modified Theory of Gravity

A self consistent system of Plane Symmetric gravitational field and a binary mixture of perfect fluid and dark energy in a modified theory of gravity are considered. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = γρ with γ∈ [0, 1] whereas, the dark energy is considered to be either the quintessence like equation of state or Chaplygin gas. The exact solutions to the corresponding field equations are obtained for power-law and exponential volumetric expansion. The geometrical and physical parameters for both the models are studied.     

Gravitational radiation of isolated systems

The gravitational radiation of isolated systems is studied by introducing a class of reference systems that is the analog of the class of inertial systems in flat space. Expressions for the total energy of these systems and the flux of gravitational radiation are obtained. The fundamental role of the Bondi-Metzner-Sachs asymptotic symmetry groups in the general theory of relativity is explained; transformations of the group characterize transitions from one reference system of a given class to another.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 47–54, November, 1973.     

Gravitational radiation of Island systems with an electromagnetic field

A study is made of the gravitational radiation of a system of bounded sources in the presence of an electromagnetic field. A class of frames of reference-analogs of inertial frames in flat space-is introduced on the basis of the criterion proposed by Dozmorov. Expressions are obtained for the total energy of such systems and the flux of gravitational radiation.     

Gravitational Corrections to Energy-Levels of a Hydrogen Atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.     

关于引力场的能量问题

本文讨论引力场中局部区域的能量问题。这里提出了一个新的引力场总能量-动量赝张量密度,它所表示的引力场局部空间区域中的能量对纯空间坐标变换是不变量,因而引力场的局部区域能量具有确定的物理意义。关于Schwarzschild场的能量和动量,新的赝张量给出的结果要比现有广义相对论文献中的其他形式的赝张量所给出的结果较为合理。文中还讨论了在引力理论中质量与能量的关系问题。 关键词：     

Energy of Gravitational Field of Static Spherically Symmetric Neutron Stars

By using the Einstein-Tolman expression of the energy-momentum pseudo-tensor, the energy density of the gravitational field of the static spherically symmetric neutron stars is calculated in the Cartesian coordinate system.It is exciting that the energy density of gravitational field is positive and rational The xmmerical results of the energy density of gravitational field of neutron stars are calculated. For neutron stars with M=2M, the ratio of the energy density of gravitational field to the energy density of pure matters would be up to 0.54 at the surface.     

The energy of the universe

The energy of the universe, including the energy of the matter and that of the gravitational field, is investigated with the help of the Einstein gravitational pseudo-tensor. It is found that the total energy vanishes.     

Energy and Momentum of Robinson-Trautman Space-Times

Robinson and Trautman space-times are studied in the context of teleparallel equivalent of general relativity (TEGR). These space-times are the simplest class of asymptotically flat geometries admitting gravitational waves. We calculate the total energy for such space-times using two methods, the gravitational energy-momentum and the translational momentum 2-form. The two methods give equal results of these calculations. We show that the value of energy depends on the gravitational mass M, the Gaussian curvature of the surfaces λ(u,θ) and on the function K(u,θ). The total energy reduces to the energies of Schwarzschild’s and Bondi’s space-times under specific forms of the function K(u,θ).     

Energy of Gravitational Field of Static Spherically Symmetric Neutron Stars

By using the Einstein-Tolman expression of the energy-momentum pseudo-tensor, the energy density ofthe gravitational field of the static spherically symmetric neutron stars is calculated in the Cartesian coordinate system.It is exciting that the energy density of gravitational field is positive and rational. The numerical results ot the energydensity of gravitational field of neutron stars are calculated. For neutron stars with M = 2M , the ratio of the energydensity of gravitational field to the energy density of pure matters would be up to 0.54 at the surface.     

The thermodynamics of a system containingn identical black holes and black-body radiation

The problem ofn identical black holes in a box separated by partitions is considered. Each black hole is in thermal equilibrium with black-body radiation. The separating partitions are removed and the possible final states of the combined system are investigated. Limits on the amount of gravitational wave energy that can be produced are calculated, and it is shown that forn large enough, as large a fraction of the initial energy as is desired may be extracted as gravitational waves.     

The Energy of the Universe in Teleparallel Gravity

The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that in the case of a closed universe, the total energy vanishes independently of the pseudotensor used, as well as of the three dimensionless coupling constants of teleparallel gravity.     

Gravitational and inertial mass of bodies of interacting electrical charges

Starting from the equations of motion of particles interacting with both electromagnetic and gravitational fields, the (passive) gravitational mass (M _g) and the inertial mass (M _i) of the total system of interacting charges is calculated. It is found that in both Einstein's General Relativity and the scalar-tensor gravitational theory of Brans and Dicke,M _g andM _i are both equal to the Special Relativistic energy of the system of interacting charged particles. Therefore, both theories are compatible with the high accuracy measurements of theM _g/M _i ratio of laboratory objects. This work was supported by National Aeronautics and Space Administration grant NGR 27-001-035.     

The gravitational field of a superconducting cosmic string

The gravitational properties of a long, straight superconducting string are discussed. It turns out that a light ray is deflected through an angle which depends on the total energy per unit length whereas the gravitational force on a test particle depends on the electromagnetic energy in the string.     

引力孤立波

本文给出了真空爱因斯坦方程的一组严格的孤立波解,证明了存在一种处处正则,稳定而不扩散且以光速传播的引力波,并对它们的奇异性和能量分布问题进行了讨论。 关键词：     

Gravitational collapse of dark energy field configurations and supermassive black hole formation

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.