爱因斯坦引力场Arnowitt-Deser-Misner约束方程的两种推导方法

给出两种不同方法,分别导出爱因斯坦引力理论中著名的Arnowitt-Deser-Misner(ADM)约束方程.其一是在具有洛伦兹号差的时空中,构造一个单参数引力场作用量,由此导出单参数ADM约束方程.该参数取某特定值时对应的就是熟知的ADM约束方程.其二是将二重复函数理论运用于爱因斯坦引力场的哈密顿形式表述中,得到引力场ADM约束的二重化形式,从而也能将通常的ADM约束作为其特殊情况包含其中.此外,这两种方法还能统一地表述具有不同时空号差(洛伦兹号差和欧几里得号差)的洛伦兹引力理论和欧几里得引力理论 关键词： Arnowitt-Deser-Misner约束方程 哈密顿表述 时空号差 引力场作用量     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

New ways of deriving Arnowitt—Deser—Misner constraint equations in four—dimensional gravity

In this paper,the Arnowitt-Deser-Misner (ADM) constraint equations are naturally derived in two different ways.One method is to construct a one-parametric gravitational action in the Lorentzian spacetime.Hence,the oneparametric ADM constraint equations can be obtained.The other method is to apply the double complex function method to Einstein-Hilbert gravitational fields in Hamiltonian formulation,Therefore the double ADM constraint equations can be obtained,in which the well-known ADM constraint equations are included as a special case.     

Initial data sets of minimal energy

The total mass of a gravitational system, the ADM mass, is considered as a functional of the initial data sets for sources and gravitation. From the condition that such a functional has a minimum under a restricted class of variations, tensorial equations for the gravitational initial data are obtained. The solutions to these equations, whose existence for a large class of source fields is asserted, represent initial data sets for gravitation satisfying the constraint equations and may be considered as having no gravitational radiation.     

Energy and momentum from the Palatini formalism

I derive from the Palatini formalism, in which metric and affinity are varied independently, an energy-momentum complex qualitatively different in form from the usual energy-momentum representations of general relativity. A similar procedure can be carried out for electrodynamics, illuminating by analogy the structure of the gravitational Lagrangian. The new energy density vanishes for all static vacuum solutions of the Einstein equations, and the radiated energy from an isolated system in an asymptotically flat space in general diverges. These facts suggest that the formalism could be used to express Mach's principle.     

On the Form of Parametrized Gravitation in Flat Spacetime

In a framework describing manifestly covariant relativistic evolution using a scalar time , consistency demands that -dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred time coordinate changes the theory significantly. In particular, the Hamiltonian constraint for is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux density only serves as the source. Building on that foundation, in this paper we develop a linear approximate theory of parametrized gravitation in the spirit of the flat spacetime approach to general relativity. Using a modified form of Kraichnan's flat spacetime derivation of general relativity, we extend the linear theory to a family of nonlinear theories in which the flat metric and the gravitational field coalesce into a single effective curved metric.     

Gravitating Hopfions

We construct solutions of the 3 + 1 dimensional Faddeev–Skyrme model coupled to Einstein gravity. The solutions are static and asymptotically flat. They are characterized by a topological Hopf number. We investigate the dependence of the ADM masses of gravitating Hopfions on the gravitational coupling. When gravity is coupled to flat space solutions, a branch of gravitating Hopfion solutions arises and merges at a maximal value of the coupling constant with a second branch of solutions. This upper branch has no flat space limit. Instead, in the limit of a vanishing coupling constant, it connects to either the Bartnik–McKinnon or a generalized Bartnik–McKinnon solution. We further find that in the strong-coupling limit, there is no difference between the gravitating solitons of the Skyrme model and the Faddeev–Skyrme model.     

Complementary aspects of gravitation and electromagnetism

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary charge), the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge.     

Sources of gravitational waves in asymptotically flat Einstein-Maxwell spacetime

In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the regularized null cone cuts equation, and the center of mass of an asymptotically flat Einstein-Maxwell spacetime are used. A set of equations are derived in the low speed regime, linking their time evolution to the emitted gravitational radiation and to the Maxwell fields received at infinity. These equations should be useful when describing the dynamic of compact sources, such as the final moments of binary coalescence and the evolution of the final black hole. Additionally, we compare our equations with those coming from a similar approach given by Newman, finding some differences in the motion of the center of mass and spin of the gravitational system.     

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.     

矢引力子场度规场引力理论的共形平直静止解及引力场的能量动量赝张量的正常性

本文求出了VGM引力理论的共形平直静止解。文中把胡宁表达式引入VGM,它同样是守恒的能量动量表达式。对于单个集中质量的引力场,与GR一样,可证实引力质量与惯性质量相等。但Einstein的等效原理在这理论中并不成立。利用所求得的解,可知当n<1/4时,引力场的能量动量赝张量就是正常的。 关键词：     

The string spectrum on the horizon of a non-extremal black hole

We investigate the conformal string σ-model corresponding to a general five-dimensional non-extremal black hole solution. In the horizon region the theory reduces to an exactly solvable conformal field theory. We determine the modular invariant spectrum of physical string states, which expresses the Rindler momentum operator in terms of three charges and string oscillators. For black holes with winding and Kaluza-Klein charges, we find that states made with only right-moving excitations have ADM mass equal to the black hole ADM mass, and thus they can be used as sources of the gravitational field. A discussion on statistical entropy is included.     

The ADM Hamiltonian at the postlinear approximation

The ADM Hamiltonian for a many-particle system is calculated up to the postlinear approximation, i.e., to the approximation that both the equations of motion for the particles and the equations of motion for the gravitational field in case of no-incoming radiation correctly result up to the postlinear approximation. The relation of this Hamiltonian to the ADM Hamiltonian obtained by a post-Newtonian approximation scheme which was applied up to the first radiation-reaction and radiation levels is discussed. From here the standard formulas for the mechanical angular momentum and energy losses as well as the radiated energy and angular momentum are deduced. Background logarithmic and logarithmic radiative terms are shown to be not present at our approximation if the condition of no-incoming radiation is fulfilled.     

Global and local horizon quantum mechanics

Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical “Hamiltonian” constraint that relates the gravitational radius to the ADM mass, thus giving rise to a “horizon wave-function”. This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner–Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.     

Centrifugal deformations of the gravitational kink

The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.     

Large numbers hypothesis. IV. The cosmological constant and quantum physics

In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.     

Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate

The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching fiat plate is solved by using the Adomian decomposition method （ADM）. The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.     

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.