A new coordinate condition,and elementary flatness,for axially symmetric interior solutions in general relativity

Two general results for stationary axially symmetric interior solutions of the Einstein or Einstein-Maxwell equations in cylindrical coordinates are derived.Firstly, a coordinate condition for interior solutions is proposed, corresponding to the Weyl coordinate condition used in the exterior.Secondly, it is shown that elementary flatness in the interior is always ensured by realistic boundary conditions and matter tensors, given elementary flatness in the exterior metric.A physical discussion of the results is given, particularly in reference to solutions which have singular struts in them.     

A new test of general relativity

The emission of gravitational radiation by the recently discovered binary pulsar system will cause its orbital periodP to decrease at a rate which can now be predicted to beP ^–1 dP/dt= –(3 ± 2) × 10^–9yr^–1 if the only orbital perturbations are of general-relativistic origin. It is shown that other sources of period change are probably less important. The accuracy of this prediction as well as the possibility of its verification will improve greatly over the next few years. This is the first observation that can test general relativity beyond the post-Newtonian approximation.Work supported in part by National Science Foundation under grant No. MPS 74-15524.This essay received the fifth award from the Gravity Research Foundation for 1975 (Editor).     

A new definition of singular points in general relativity

To any space time a boundary is attached on which incomplete geodesics terminate as well as inextensible timelike curves of finite length and bounded acceleration. The construction is free ofad hoc assumptions concerning the topology of the boundary and the identification of curves defining the same boundary point. Moreover it is a direct generalization of the Cauchy completion of positive definite Riemannian spaces.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General Relativity     

McGuire-Ruffini solution in new general relativity

We obtain a solution of new general relativity from a solution of Einstein's general relativity which includes many known solutions, such as Kerr-Newman-Kasuya, Kerr-Newman, Kerr, and NUT, as special cases.     

Energy localization in general relativity: A new hypothesis

A new hypothesis for energy localization in general relativity is introduced which is based upon the fact that the energy-momentum conservation laws are devoid of content in vacuum. The vanishing of pseudotensor components forms the basis of coordinate conditions consistent with the above. The implication is that energy is localized where the energy-momentum tensor is nonvanishing. As a consequence, gravitational waves are not carriers of energy in vacuum. A detailed analysis of a Feynman detector interacting with a plane gravitational wave is consistent with the hypothesis. The fact that there has never been a confirmed direct energy transfer to a detector via gravitational radiation is also consistent with the hypothesis.     

Method for analyzing coordinate singularities in the general theory of relativity

A general method for analyzing singularities of metrics is developed. Metrics are regularized and invariant operations are calculated, which must not change with regularization. This method is inspected in relation to the Schwarzschild metric.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 42–45, March, 1987.     

Classical and quantum general relativity: A new paradigm

We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework. Fifth Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

A new approach to the problem of motion in general relativity

The dynamical meaning of the equationsT ^/j/ij =0 is derived as a consequence of the mathematical structure of Einstein's equations. A generalization of Lichnerowicz's analysis of the gravitational equations is proposed.Lavoro eseguito nel centro di Matematica e Fisica Teorica del C.N.R. presso l'Università di Genova.     

A new Hamiltonian structure for the dynamics of general relativity

A new compact form of the dynamical equations of relativity is proposed. The new form clarifies the covariance of the equations under coordinate transformations of the space-time. On a deeper level, we obtain new insight into the infinite-dimensional symplectic geometry behind the dynamical equations, the decompositions of gravitational perturbations, and the space of gravitational degrees of freedom. Prospects for these results in studying fields coupled to gravity and the quantization of gravity are outlined.This essay was awarded the second prize for 1976 by the Gravity Research Foundation.     

A nonintegrable model in general relativity

The geodesic flow of a perturbation of the Schwarzschild metric is shown to possess a chaotic invariant set. The perturbed meric is a relativistic analogue of Hill's problem in classical celestial mechanics in that is models the effects of a distant third body.Supported by the National Science Foundations and the Forschungsinstitut für Mathematik, ETH, Zürich     

ORTOCARTAN — A new computer program for analytic calculations in general relativity

This paper is meant to announce the appearance of a new computer program for symbolic calculations in general relativity, named ORTOCARTAN. The program calculates the curvature quantities from an orthonormal tetrad of forms representing the metric, both the tetrad and the coordinate components. The paper describes the main features of the program's input and output, and compares the program's speed to a few general-purpose systems, notably LAM, ALTRAN, FORMAC, REDUCE, and SYMBAL. A general overview of technical parameters of the program, and conceptual features of the algorithm is given.     

MALBEC: a new CUDA-C ray-tracer in general relativity

A new CUDA-C code for tracing orbits around non-charged black holes is presented. This code, named MALBEC, take advantage of the graphic processing units and the CUDA platform for tracking null and timelike test particles in Schwarzschild and Kerr. Also, a new general set of equations that describe the closed circular orbits of any timelike test particle in the equatorial plane is derived. These equations are extremely important in order to compare the analytical behavior of the orbits with the numerical results and verify the correct implementation of the Runge–Kutta algorithm in MALBEC. Finally, other numerical tests are performed, demonstrating that MALBEC is able to reproduce some well-known results in these metrics in a faster and more efficient way than a conventional CPU implementation.     

A new approach to the theory of relativity. II. The general theory of relativity

The considerations of Part I are extended and the experimental data and hypotheses that led to the establishment of the general theory of relativity are analyzed. It is found that one of the fundamental assumptions is that light is propagated homogeneously; i.e., by using arbitrary systems of coordinates, propagation of light can be represented by a homogeneous quadratic form. This is shown to be an assumption that can be verified by experiment, at least in principle. As a result of adding a number of further assumptions to this, the usual formalism of the general theory of relativity can be established. In the above point of view, the general theory of relativity—like any other theory—cannot be built upad hoc, but is built on distinct physical hypotheses, each of which can be subjected to test by experiment.     

Proposed new test of spin effects in general relativity

The recent discovery of a double-pulsar PSR J0737-3039A/B provides an opportunity of unequivocally observing, for the first time, spin effects in general relativity. Existing efforts involve detection of the precession of the spinning body itself. However, for a close binary system, spin effects on the orbit may also be discernible. Not only do they add to the advance of the periastron (by an amount which is small compared to the conventional contribution) but they also give rise to a precession of the orbit about the spin direction. The measurement of such an effect would also give information on the moment of inertia of pulsars.     

A singularity-free particle model in general relativity

In general relativity a general static solution describing spherically symmetric distributions of scalar and electrically charged dust is obtained and applied to the construction of a singularity-free extended particle model.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

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.