A new coordinate condition in general relativity

In this paper, a new coordinate condition in general relativity is proposed. This coordinate condition is just Euler's equations of the harmonic map theory. It is shown that in case of rectangular coordinates our coordinate condition reduces to Fock's harmonic coordinate condition. Using this new coordinate condition the different spherical symmetric solutions of the Einstein equations are discussed. The axisymmetric case is also investigated.     

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 solution for a charged sphere in general relativity

In the present paper the field equations of general relativity have been solved to obtain a solution for a static charged fluid sphere. This solution is free from singularity and satisfies the necessary physical conditions.     

An exact solution for uniformly accelerated particles in general relativity

Recently an exact solution of Einstein's empty-space equations referring to four uniformly accelerated particles was given. The relation of this to static axially symmetric metrics of the Weyl and Einstein-Rosen classes is investigated in the present paper. A physical interpretation of the singularity along half of the axis of symmetry of the uniformly accelerated metric in Weyl's form is given. An exact solution corresponding to an expanding (contracting) singular null surface is obtained by a limiting process from that for uniformly accelerated particles.     

An exact solution for uniformly accelerated particles in general relativity

We present an exact solution of the Einstein empty-space equations referring to four particles in relative motion. The particles move with different uniform accelerations relative to a co-ordinate system which is Minkowskian at infinity, except in certain directions. If positive and negative masses are allowed, the particles can move freely under their own gravitation; if all four masses are positive, stresses extending to infinity are needed to cause the motion, but two of the particles can move freely. There are three results of interest. First, the field can be described in terms of a classical potential which is the average of retarded and advanced potentials corresponding to the particles. Secondly, the field at spatial infinity is entirely different from that of a static mass, and theg _ik fall off like the inversesquare of the distance. Thirdly, the world-lines of free particles are geodesics of the space-time.     

Exact solution of a static charged sphere in general relativity

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass. Their physical properties are studied in some detail. Our solution includes as special cases the results given previously by Cooperstock and De La Cruz, Mehra and Bohra, Santos, and Shi-Chang.     

Spherically symmetric solution in higher-dimensional teleparallel equivalent of general relativity

A theory of(N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity(TEGR).The fundamental gravitational field variables are the(N+1)-dimensional vector fields,defined globally on a manifold M,and the gravitational field is attributed to the torsion.The form of Lagrangian density is quadratic in torsion tensor.We then give an exact five-dimensional spherically symmetric solution(Schwarzschild(4+1)-dimensions).Finally,we calculate energy and spatial momentum using gravitational energy-momentum tensor and superpotential 2-form.     

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.     

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 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     

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.     

Exact solution for a static charged gas sphere in general relativity

A general solution of the Einstein-Maxwell field equations has been obtained for a static charged gas sphere having maximum matter density at the centre. The density decreases along the radius and finally becomes zero at the surface of the sphere.     

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.     

Limiting transitions in the Tolman solution of the equations of general relativity

The paper considers the limiting transitions to special relativity and the Newtonian theory of gravitation in the Tolman solutions of the Einstein equations. It is shown that elliptical systems do not have an analog in the special theory. The analogs for hyperbolic and parabolic systems are the noninertial Robertson and the special-theory inertial systems, respectively. It is shown that a transition to the Newtonian theory of gravitation can be made for any type of Tolman coordinate system.     

Linearized solution of isentropic motions of a perfect fluid in general relativity

Isentropic motions of a perfect fluid are studied by using comoving coordinates in the framework of general relativity without assuming any symmetry in the line element and a linearized solution is obtained by dealing with the Cauchy problem.     

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.     

A solution for a family of perfect fluid cylinders in general relativity

A static solution of Einstein's equations representing perfect fluid cylinders of finite radius is presented. The density and pressurep are finite and monotonic decreasing from the axis to the boundary. The ratiop/ (< 1) also decreases steadily. The regularity condition at the axis is satisfied and the solution is free of singularity. The equation of state is found and special cases considered. It is shown that the solution can be joined to the vacuum cylindrical metric at the boundary. There is then at least one free parameter left in the family of solutions.     

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     

Scalar torsion and a new symmetry of general relativity

We reformulate the general theory of relativity in the language of Riemann–Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to Riemann–Cartan space-times with scalar torsion and obtain the conservation laws for auto-parallel motions in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.