与额外维相关的膜宇宙模型

对引力场的能量\|动量和角动量守恒定律研究进展进行了总结。依此探讨了一般五维时空膜宇宙模型中的能量\|动量张量、 角动量张量以及它们的守恒定律。通过计算一个膜宇宙模型中的能动张量, 论证了该模型中“可见膜”上的引力非常弱, 这可认为是从引力的角度反映了规范层次问题。结果与一般的结论, 即引力系统总能量为零是一致的。同时, 分析了这个膜宇宙模型中的角动量张量, 计算了该模型中的总角动量, 讨论了暴涨Randall\|Sundren(RS)模型中的总角动量的一些性质。说明了在这类模型中总角动量的类空分量均为零, 这与普通RS模型是一样的。同时, 分析了RS模型中背景以及膜上的宇宙学常数, 发现在RS模型中五维背景宇宙学常数和两个膜上的真空能都能取它们的自然值。最后通过修改RS模型, 得到了一种可以产生很小的有效宇宙学常数的机制。We summarized both the general covariant energy\|momentum and angular momentum conservation law in the gravitational system and analyzed the general covariant energy\|momentum tensor of the gravitational system in general five\|dimensional cosmological in brane\|universe models. After calculating this energy\|momentum for the cosmological generalization of the Randall\|Sundrum(RS) 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. We also discussed the properties of the general covariant angular momentum in five\|dimensional brane-universe model. With calculation of the total angular momentum of this model, we analyzed the properties of the total angular momentum in the inflationary RS model. We pointed that the space-like components of the total angular momentum are zero while the others are non-zero, which agrees with the results from ordinary RS model. We also investigated the bulk cosmological constant and brane vacuum energies in RS model. We show that the five\|dimensional bulk cosmological constant and the vacuum energies of the two branes could take their natural values. Finally we argued how we can generate a small four-dimensional effective cosmological constant on the branes by modifying the original RS model.     

On the energy-momentum and spin tensors in the Riemann–Cartan space

General classical theories of material fields in an arbitrary Riemann–Cartan space are considered. For these theories, with the help of equations of balance, new non-trivially generalized, manifestly generally covariant expressions for canonical energy-momentum and spin tensors are constructed in the cases when a Lagrangian contains (a) an arbitrary set of tensorial material fields and their covariant derivatives up to the second order, as well as (b) the curvature tensor and (c) the torsion tensor with its covariant derivatives up to the second order. A non-trivial manifestly generally covariant generalization of the Belinfante symmetrization procedure, suitable for an arbitrary Riemann–Cartan space, is carried out. A covariant symmetrized energy-momentum tensor is constructed in a general form.     

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.     

Gravitational Energy-Momentum and Conservation of Energy-Momentum in General Relativity

Based on a general variational principle, Einstein-Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a result of mistaking different geometrical, physical objects as one and the same. It is also pointed out that in a curved spacetime, the sum vector of matter energy-momentum over a finite hyper-surface can not be defined. In curvilinear coordinate systems conservation of matter energy-momentum is not the continuity equations for its components. Conservation of matter energy-momentum is the vanishing of the covariant divergence of its density-flux tensor field. Introducing gravitational energy-momentum to save the law of conservation of energy-momentum is unnecessary and improper. After reasonably defining “change of a particle’s energy-momentum”, we show that gravitational field does not exchange energy-momentum with particles. And it does not exchange energy-momentum with matter fields either. Therefore, the gravitational field does not carry energy-momentum, it is not a force field and gravity is not a natural force.     

General Covariant Conservation Law of Energy-Momentum in f(R) Gravity

In the light of the local Lorentz transformations and the general Noether theorem, a new formulate of the general covariant energy-momentum conservation law in f(R) gravity is obtained, which does not depend on the coordinative choice.     

Conservation laws in the tetrad formulation of the general theory of relativity

The covariant consequences of a weak conservation law in the tetrad formulation of general relativity that do not contain noncovariant complexes of energy-momentum or external and internal spin momenta are considered. The relationship between a group of arbitrary tetrad Lorentz transformations and a generally covariant definition of the spin angular momentum of nongravitational matter is outlined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 101–105, February, 1979.     

Inertia and Gravity: a New Approach to Dynamical Theory in General Relativity

A new approach to gravitational field dynamics is proposed, as an alternative to the standard formulation of General Relativity. The spacetime metric tensor is split, into an externally fixed background geometry (inertia) and a local dynamical field (gravity); and a dynamical theory of matter and gravity in the inertial background is developed. The physical origin of inertia (Mach's Principle), and its observable properties, are discussed. The coordinate representations of inertia and gravity are found to have an internal gauge degree of freedom, due to the Equivalence Principle; the transformation properties of these fields, and the notion of covariant gauge conditions, are discussed. The dynamics of matter and gravitic fields is then investigated, using: (i) The group of motion of the inertial background, appearing as an externally fixed Lie symmetry in the matter and gravity action principles, which yields weakly conserved energy-momentum-like objects; and (ii) an internal symmetry gauge group, yielding strongly conserved “internal currents”. A fully covariant field-theoretical formalism is used, in which all quantities and operations are tensorial; the well-known difficulties of “coordinate effects” in the standard nontensorial formulation are thus avoided. The physical significance of various types of conservation laws is discussed; and a complete family of energy-momentum tensors of gravity, covariantly conserved together with the matter energy-momentum, is deduced from a tensorial action principle. Treating gravity as an independent dynamical interaction, on an equal footing with other (matter) interactions, we are then finally led to the conclusion that the gravitic energy-momentum of a system is fully determined by the matter energy-momentum; various physical implications of this are discussed in some detail.     

评“Einstein-Cartan引力理论中的广义协变守恒定律”

本文证明:如果以坐标的广义位移变换和标架场的Lie微商作为对称变换,则不可能利用Noether定理得出所谓Einstein-Cartan引力理论中广义协变的能量动量守恒定律。 关键词：     

Two theorems on energy-momentum conservation

The mathematical meaning of the law of conservation of energy-momentum is examined. A distinction is made between the intrinsic properties of the metric tensor (i.e., those properties that are independent of the coordinate system), and the nonintrinsic properties of this tensor (i.e., those properties that depend upon the coordinate system). The covariance of the energy-momentum law is used to demonstrate that if one is given (a) any analytic contravariant energy-momentum tensor density in a given coordinate systemx and (b) an analytic specification of the intrinsic properties of the metric tensor, no matter what these properties may be, one can always choose the nonintrinsic properties of the metric tensor in such manner as to satisfy the law of conservation of energy-momentum in the coordinate systemx and thereby in every coordinate system. This result is proved only in the case where the contravariant components of the energy-momentum tensor density are given. Neither the covariant, nor the mixed energy-momentum tensor densities are considered. Other theorems similar to that described above are also derived. Many of the results obtained are nontrivial even when space-time is flat.     

Covariant Anomalies and Functional Determinants

We analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations by means of functional determinants, showing how the algebraic solution determines the relevant operators for the definition of the effective action. Particular attention is devoted to the Lorentz anomaly: we obtain by functional methods the covariant anomaly for the spin-current and for the energy-momentum tensor in presence of a curved background. With regard to the consistent sector we are able to give a general functional solution only for d = 2: using the characterization derived from the extended algebra, we find a continuous family of operators whose determinant describes the effective action of chiral spinors in curved space. We compute this action and we generalize the result in presence of a U(1) gauge connection.     

CONFORMALLY COVARIANT THEORY OF SECOND RANK ANTISYMMETRIC TENSOR FIELD

The conformally covariant field equation on second rank antisymmetric tensor is derived and its conformally covariant energy-momentum tensor is also obtained.     

Some remarks on the energy-momentum tensor in general relativity

In general relativity, the energy-momentum tensor of a classical tensor field can be constructed by varying the action of the field with respect to the background metric. This paper suggests an alternative interpretation of the construction which also makes sense for spinor fields, and which gives some insight into the locality of energy-momentum operators in generally covariant quantum field theory.     

Cosmology of general relativity without energy-momentum conservation

A modified version of the field equations of general relativity is obtained on relaxing the covariant energy-momentum conservation condition. This introduces a single arbitrary constant and does not appear to upset the successes of general relativity in or outside cosmology. The matter-dominated cosmological model, based on the generalized field equations, is discussed. It is shown to provide more room for consistency with the observational data.     

Covariant formulation of the weak conservation law in the general theory of relativity without the energy-momentum of the gravitational field

A systematic covariant formulation is given of the weak conservation law in the general theory of relativity for arbitrary coordinate transformations without introducing the unsatisfactory definition of the energy-momentum of the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 13–16 July, 1979.     

Einstein-Cartan引力理论中的广义协变守恒定律

本文从广义Noether定理出发,对Einstein-Cartan引力理论中一般拉氏量所对应的守恒定律作了普遍的讨论,并由广义位移交换x^μ＇=x^μ+e_d^μb^a得到了包含挠率的一般拉氏密度所对应的广义协变能量动量守恒定律,并论述了超势存在的必然性。它是文献[1]和[2]理论的自然推广。 关键词：     

Gravitational energy and momentum: A tensorial approach

A tensorial expression for localized gravitational energy-momentum is delineated as an integral part of the energy-momentum tensor. A bona fide conservation law of the total energy-momentum tensor is obtained in the geodesic-nonrotating coordinates, in which the covariant divergencelessness of the energy-momentum tensor reads, globally, as ordinary divergencelessness. The integral gravitational energy in the exterior of a spherically symmetric source is calculated based on this tensorial relativistic expression. For an ordinary star, such as the sun, it coincides with the Newtonian value up to six digits.     

Covariant construction of the symmetric energy-momentum tensor of vector and spinor fields in an orthogonal frame of reference

A covariant method is devised to construct the symmetric energy-momentum tensor for vector fields in an orthogonal frame of reference. The method is then used to construct the symmetric energy-momentum tensor for spinor fields. Kazan’ University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, March, 1997.     

Relation between quasirigidity andL-rigidity in space-times of constant curvature and weak fields

The relation between quasirigidity andL-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, underL-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus,L-rigidity leads to quasirigidity in such space-times.     

Derivation and uniqueness of vacuum solutions of conformally covariant coupled nonlinear field equations

We derive the solutions of conformally covariant coupled Dirac and scalar fields including a nonlinear fermion self-coupling term for which the conformally covariant (not the canonical, nor the symmetric) energy-momentum tensor θ_μν vanishes. This “vacuum” state is degenerate.     

A quadratic spinor Lagrangian for general relativity

We present a newfinite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof, is fully 4-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof.This essay received the fourth award from the Gravity Research Foundation, 1994—Ed.