Kinks in general relativity

The problem of classifying topologically distinct general relativistic metrics is discussed. For a wide class of parallelizable space-time manifolds it is shown that a certain integer-valued topological invariant n always exists, and that quantization when n is odd will lead to spinor wave functionals.     

Time in general relativity

In order to distinguish between physical and coordinate effects in an arbitrary gravitational field, the space coordinate system and the clock rates must be specified operationallya priori. Once this is done, it is no longer possible to set up an initial surface arbitrarily, since this operation must be consistent with certain physical experiments, whose results depend upon the particular physical situation. A method is given for setting up the initial surface, and the time evolution of the system is discussed.NASA Predoctoral Fellow.     

Conventionalism and general relativity

We argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of spacetime, only the behavior of matter in space and time. General relativity is then rewritten in terms of an arbitrary conventional geometry of spacetime in which particle trajectories are determined by forces in that geometry, and the forces determined by fields produced by sources in that geometry. As an example, we consider radial trajectories in the field of a single particle expressed in the spacetime of special relativity.     

Tachyons in general relativity

The tachyonic version of the Schwarzschild (bradyonic) gravitational field within the framework of extended relativity is considered. The metric of a tachyonic black hole is obtained through superluminal transformations from a bradyonic metric. The extended space-time manifold of this geometry which includes both black and white tachyonic holes is analysed, and the differences between the tachyonic and bradyonic versions are noted. It is shown that the meanings of black holes, tachyons and bradyons depend on the character of the reference frame and are not absolute.     

Singularities in general relativity

The problem of singularities is examined from the stand-point of a local observer. A singularity is defined as a state with an infinite proper rest mass density. The approach consists of three steps: (i) The complete system of equations describing a non-symmetric motion of a perfect fluid under assumption of adiabatic thermodynamic processes and of no release of nuclear energy is reduced to six Einstein field equations and their four first integrals for six remaining unknown componentsgik. (ii) A differential relation for the behavior of the rest mass density is deduced. It shows that any inhomogeneity and anisotropy in the distribution and motion of a non-rotating ideal fluid accelerates collapse to a singularity which will be reached in a finite proper time. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In the case of a lower or zero pressure the relation does not give an unambiguous answer if the matter is rotating. (iii) The influence of rotation on the motion of an incoherent matter is investigated. Some qualitative arguments are given for a possible existence of a narrow class of singularity-free solutions of Einstein equations. Assuming rotational symmetry the Einstein partial differential equations together with their first integrals are reduced to a system of simultaneous ordinary differential equations suitable for numerical integration. Without integrating this system the existence of the class of singularity-free solutions is confirmed and exactly delimited. These solutions, representing a new general relativistic effect, are, however, of no importance for the application in cosmology or astrophysics. It is proved that in all the other cases interesting from the point of view of application the occurrence of a point singularity in incoherent matter with a rotational symmetry is inevitable even if the rotation is present.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General Relativity     

Lattice formulation of general relativity

It is shown that almost the entire excitation energy acquired by the fission fragments during the descent from the saddle to the scission point comes from Landau-Zener transitions. The states tractable in the first order adiabatic approximation carry an excitation energy of a few hundred keV.     

An axiomatization of general relativity

An axiomatization of the general theory of relativity is proposed. The assumed philosophical background is critical realism. None of the principles commonly considered as founding the theory, such as (a) the equality of inertial and gravitational mass, (b) the principle of equivalence, (c) the principle of general covariance, (d) the geodesic postulate, and (e) Mach's principle, are taken as axioms in our system.     

The regimen of general relativity

New developments in our understanding of the electron-atom collision process have been made possible by combining the use of highly monochromatic electron beams and intense CO₂ lasers. This paper reviews such experiments and discusses possible future progress in what is a new field in atomic collision physics.     

爱因斯坦与广义相对论

文章介绍了爱因斯坦建立相对论,特别是广义相对论的伟大贡献。爱因斯坦提出了光速不变原理、广义相对性原理、马赫原理和等效原理。他不仅首先指出万有引力本质上是时空弯曲的几何效应,而且首先给出了广义相对论的基本方程。文章还讨论了为什么爱因斯坦是狭义相对论和广义相对论的唯一创建者。     

Junction conditions in general relativity

We examine the three sets of junction conditions commonly used in general relativity: those due to Darmois, to O'Brien and Synge, and to Lichnerowicz. We show that those due to Darmois and Lichnerowicz are equivalent. The O'Brien and Synge set is stronger than the other two and is unsatisfactory in that it may rule out physically plausible junctions. We conclude that the Darmois set is the most convenient and reliable.     

Nongeodesic motion in general relativity

The equations of motion of a spinning body in the gravitational field of a much larger mass are found using both the Corinaldesi-Papapetrou spin supplementary condition (SSC) and the Pirani SSC. These equations of motion are compared with our previous result derived from Gupta's quantum theory of Gravitation. It is found that the spin-dependent terms differ in each of the above three results due to a different location of the center of mass of the spinning body. As expected, these terms are not affected by the choice of either Schwarzschild or isotropic coordinates. Finally, for the presently planned Stanford gyroscope experiment, we find the maximum secular displacement of the orbit of the gyro with respect to the orbit of its non-rotating housing to be of the order of (10⁻⁷ cm/year)t, a result much smaller than Schiff's result which is proportional to time squared.     

Algebraic computing in general relativity

The purpose of this paper is to bring to the attention of potential users the existence of algebraic computing systems, and to illustrate their use by reviewing a number of problems for which such a system has been successfully used in General Relativity. In addition, some remarks are included which may be of help in the future design of these systems.     

Acceleration-dependent lagrangians in general relativity

In contrast to electromagnetic theory, in general relativity the elimination of acceleration terms in a lagrangian by substituting into the lagrangian the equations of motion which follow from the lagrangian is a correct procedure; it corresponds to a gauge transformation.     

The gauge in general relativity

The view is taken that the field equations of General Relativity, without a definition of congruence of length and time intervals at different events, are without physical content. The possibility is explored that the customary Einstein field equations are to be used but with a different congruence definition than is customary. When these resulting equations are, in turn, expressed with the customary congruence, they comprise a new set of field equations physically not equivalent to either Einstein's or Brans-Dicke's formulations of general relativity. Similarities with Einstein's and Brans-Dicke's formulations are discussed, and the possibility of experimental confirmation of these new equations is also briefly considered.     

Improved Hamiltonian for general relativity

A Hamiltonian formalism for asymptotically flat spaces in general relativity which is manifestly covariant under Poincaré transformations at infinity is proposed and some of its implications are briefly discussed.     

Bimetric general relativity and cosmology

A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensorg _v describing the space-time geometry and gravitation, there exists also a background metric tensor _v The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k=1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. One can set up simple isotropic closed models of the universe which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order ofc ^{5 –1} G ^–210⁹³ g/cm³. The expansion from such a high-density state is similar to that from the singular state (big bang) of the general relativity models. In the case of the dust-filled model one can fit the parameters to present cosmological data. Using the radiation-filled model to describe the early history of the universe, one can account for the cosmic abundance of helium and other light elements in the same way as in ordinary general relativity.     

Spin dynamics in general relativity

The energy-momentum tensor of a fluid composed of spinning particles is presented in a form that is structurally similar to that of a fluid with the energy flux q^a with respect to the fluid velocity u^a, isotropic pressure p and the trace-free anisotropic pressure π^ab. The effect of spin in the evolution of a shear free cosmological model with irrotational geodesic flow is considered.