Showing papers on "Introduction to the mathematics of general relativity published in 1973"
Journal Article•
383 citations
TL;DR: In this article, the authors define multipole moments of the energy-momentum tensor tensor of an extended body in general relativistic theory by studying the corresponding Newtonian theory.
Abstract: There is considerable freedom in the definition of multipole moments of the energy-momentum tensor of an extended body in general relativity. By studying the corresponding Newtonian theory we obtain guidelines which enable us to choose the most suitable definitions in the relativistic theory. In this way we find two sets, the complete moments and the reduced moments, of which the latter are the most natural choice for studying the dynamics of extended bodies. Expressions as explicit integrals are give for both sets, and the multipole equations of motion of the body are given in a form exact to all orders. Proofs of the relativistic results will appear elsewhere.
105 citations
TL;DR: In this article, strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed are presented, which limit perturbations of non-flat closed initial solutions.
Abstract: There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.
101 citations
72 citations
TL;DR: In this paper, the five-dimensional relativity theory proposed by Kaluza is formulated covariantly for a Riemannian space containing a Killing geodesic vector field, from which a four-dimensional physical space is extracted.
Abstract: The five-dimensional relativity theory proposed by Kaluza is formulated covariantly for a Riemannian space containing a Killing geodesic vector field. From this five-dimensional space a four-dimensional physical space is extracted. The field equations in empty 5-space are essentially uniquely determined and correspond to the Einstein-Maxwell equations in 4-space. In the presence of a field in 5-space the field equations involve a tensor which is associated with energy, momentum, charge and current densities in 4-space. For a 5-space containing dust the field equations lead to particle motion described by the geodesic equations. The latter correspond in 4-space to the Lorentz equations of motion for particles with arbitrary ratios of charge to mass and also for certain entities (tachyons and luminons) unobserved hitherto.
33 citations
01 Jan 1973
TL;DR: The nature and role of the various relativity principles has been correspondingly unclear as discussed by the authors, and exactly how they are associated with given physical theories, has been far from clear, as well as the nature of the role of these principles.
Abstract: Traditionally, certain physical theories have been thought to have relativity principles associated with them. Associated with Newtonian mechanics is the principle of Galilean relativity, associated with special relativity is the special or restricted principle of relativity, associated with general relativity is the general principle of relativity, etc. Such relativity principles are often expressed in terms of groups of transformations. The principle of Galilean relativity is expressed by the ‘invariance’ of Newtonian mechanics under the Galilean group, that of special relativity by the ‘invariance’ of special relativity under the Lorentz group, and that of general relativity by the ‘invariance’ (or ‘covariance’) of general relativity under the group of all 1–1 transformations with non-vanishing Jacobian. Unfortunately, just what these various groups are groups of, and exactly how they are associated with given physical theories, has been far from clear. Similarly, the nature and role of the various relativity principles has been correspondingly unclear.
25 citations
TL;DR: In this article, it was pointed out that if one did not know the Einstein-HamiltonJacobi equation one might hope to derive it straight off from plausible first principles, without ever going through the formulation of the Einstein field equations themselves.
Abstract: It is pointed out that if one did not know the Einstein--HamiltonJacobi equation one might hope to derive it straight off from plausible first principles, without ever going through the formulation of the Einstein field equations themselves. (auth)
25 citations
TL;DR: In this article, a kinetic model is used to show how the Einstein and Maxwell field equations must be modified in the presence of a medium where the particles have internal spin, and the resulting equations form an extension into general relativity of Lorentz's dielectric theory.
Abstract: A kinetic model is used to show how the Einstein and Maxwell field equations must be modified in the presence of a medium where the particles have internal spin. The resulting equations form an extension into general relativity of Lorentz's dielectric theory. (FR)
25 citations
TL;DR: In this article, it was shown that an analogue of Birkhoff's theorem of general relativity (1927) exists in a scalar-tensor theory of gravitation proposed by Sen and Dunn (1971).
Abstract: It is shown that an analogue of Birkhoff's theorem of general relativity (1927) exists in a scalar-tensor theory of gravitation proposed by Sen and Dunn (1971). Unlike in the Brans-Dicke scalar-tensor theory (1961), Birkhoff's theorem is valid in the present theory irrespective of the nature of the scalar field introduced.
21 citations
TL;DR: In this article, all space-times admitting a neutrino field having a zero energy-momentum tensor are found, and one of the space times is shown to admit two distinct neutrinos fields.
Abstract: All space-times admitting a neutrino field having a zero energy-momentum tensor are found. One of the space-times is shown to admit two distinct neutrino fields.
19 citations
TL;DR: In this article, the concept of ''future timelike infinity'' for certain space-times is defined and applied to many exact and approximate solutions of the Einstein equations. But some physical restrictions are necessary.
Abstract: We use a projective structure to make precise the concept of ``future timelike infinity'' for certain space‐times. We apply our definitions to many exact and approximate solutions of the Einstein equations. Some physical restrictions are necessary.
TL;DR: In this paper, minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b k σ n σ σ μ, which are necessary to describe the gravitational interaction of the spin 1/2 field, and they carry out the extension of the conventional tetrad formalism of general relativity.
Abstract: Minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b
k
μ, which are necessary to describe the gravitational interaction of the spin 1/2 field. For this purpose we carry out the extension of the conventional tetrad formalism of general relativity. Our general framework contains four arbitrary parameters; one of them represents the asymmetry of the affine connection (or equivalently that of the energymomentum tensor) and the others measure possible deviations from Einstein's gravitational Lagrangian, which will be responsible for spin effects. We also discuss the physical meaning of the invariance requirement with respect to the Poincare gauge transformation that uniquely leads us within the present framework to Einstein's theory of gravity.
TL;DR: In this paper, the field equations governing perturbations of a spherical star in general relativity are solved by means of a weak field or Born approximation, and formal expressions for the far field of a non-stationary source are obtained and used to discuss the Newman-Penrose constants.
Abstract: The field equations governing perturbations of a spherical star in general relativity are solved by means of a weak field or Born approximation. Formal expressions for the far field of a non-stationary source are obtained and used to discuss the Newman-Penrose constants.
TL;DR: In this paper, all asymptotically flat space solutions of Einstein equations with energy-momentum tensor of electrostatic and zero-mass scalar static central symmetric fields as a source were found.
Abstract: All asymptotically flat space solutions of Einstein equations with energy-momentum tensor of electrostatic and zero-mass scalar static central symmetric fields as a source were found. There are five branches of general solution; only two of them are contained in previous Penney's solution. In a limit of pure electrostatic field and pure scalar field our solutions become identical with corresponding solutions known previously.
TL;DR: In this article, the Lorentz-covariant two-body problem was shown to be solvable for straight-line motiom and admits solutions in which the charges move in circles about a commom center.
Abstract: S>We treat a Lorentz-covariant two-body problem due to Fokker: One electric charge experiences the retarded field of a second, while the he first; this is pure action at a distance, with no self-action; conservation principles exist. We show that this (apparently generally soluble) time-asymmetric problem is exactly soluble for straight-line motiom and admits solutions in which the charges move in circles about a commom center. We briefly consider nonelectrodynamic time-asymmetric interactions and aspects of quantizing thc motions. (auth)
TL;DR: In this article, conditions are found that are sufficient to insure the development of trapped surfaces in space-times whose metrics satisfy the Einstein field equations in vacuum or in the presence of a massless scalar field.
Abstract: Conditions are found that are sufficient to insure the development of trapped surfaces in space‐times whose metrics satisfy the Einstein field equations in vacuum or in the presence of a massless scalar field. These conditions involve a topological requirement that a certain two‐surface be compact and inequalities that must be satisfied by certain pieces of the characteristic data determining these space‐times. It is shown that a particular piece of data playing an important role in these inequalities is related to angular momentum.
TL;DR: In this article, it was shown that the definition of the velocity of a test particle in a Schwarzachild field, as measured by a distant observer, is complete, and that this definition reflects the fact that round-trip times-of-flight of fast test particles will be longer under general relativity than under Minkowskian or Newtonian theory.
Abstract: The definition we previously introduced to describe the velocity of a test particle in a Schwarzachild field, as measured by a distant observer, is shown to be complete. As we desired, this definition reflects the fact that round-trip times-of -flight of fast test particles will be longer when governed by general relativity than when governed by a Minkowskian or Newtonian theory. In this sense, particles obeying general relativity appear to slow down. Thc altemate definition of particle velocity proposed by Baierlein does not have this property and is shown to be more appropriate for a local observer than for a distant observer. (auth)
Journal Article•
TL;DR: In this article, the Einstein-Maxwell equations corresponding to a nonstatic spherically symmetric distribution of charged dust are studied and the general solution is presented in an implicit form.
Abstract: The Einstein- Maxwell equations corresponding to a nonstatic spherically symmetric distribution of charged dust is studied and the general solution is presented in an implicit form. The solutions are matched over a boundary to the Reissner-Nordstroem solution, and the equations governing the collapse are examined. The general solution to find the conditions on the parameters that will allow a gravitational bounce for a particular comoving layer is examined. (auth)
TL;DR: In this paper, a general expression for spherically symmetric distributions of non-charged, perfect fluid in general relativity is given under the assumption that the space-time is conformally flat.
Abstract: When we study spherically symmetric distributions of non-charged, perfect fluid in general relativity, a general expression giving the metric can be obtained under the assumption that the space-time is conformally flat. Formulae for the metric, matter density and pressure are given in isotropic coordinates.
TL;DR: In this paper, it was shown that the deDonder conditions can be satisfied if and only if the stress energy tensor of the sources of the gravitational field is covariantly conserved.
Abstract: We show that when the Einstein field equations for the gravitational field are modified by imposing the deDonder coordinate conditions these equations can be ‘solved’ in terms of source functions using the retarded Green's function for the d'Alembertian in flat space. The ‘solution’, which becomes an actual solution in the fast-motion approximation, is shown to satisfy the deDonder conditions if and only if the stress-energy tensor of the sources of the gravitational field is covariantly conserved. It is also shown to satisfy the Trautman outgoing radiation condition.
TL;DR: In this article, the properties of the most general (infinitesimal) mapping in phase space which preserves a congruence of classical trajectories have been determined, and the application of these results to the problem of determining the observables of the general theory of relativity is indicated.
Abstract: We determine the properties of the most general (infinitesimal) mapping in phase space which preserves a congruence of classical trajectories. Although such mappings need not be canonical, we find that they can nevertheless be associated in a unique fashion with constants of the motion. The application of these results to the problem of determining the observables of the general theory of relativity is indicated.
TL;DR: In this article, a new proof of some puzzling recent theorems on redundancy of constraints in gravitation theory is given, which is based on the inelevancy of the choice of coordinates on the surface on which the field state is defined.
Abstract: A new proof of some puzzling recent theorems on redundancy'' of constraints in gravitation theory is given. In light of this proof, the theorems are seen to be merely a consequence of the inelevancy of the choice of coordinates on the surface on which the field state is defined. It is concluded that the theorems in question are deprived of dynamical content and that they do not reduce the number of independent constraints in any physically meaningful way. The analysis applies equally well to general relativity and to parametrized field theories. (auth)
TL;DR: In this paper, it was shown that the Brans-Dicke equations do not admit everywhere regular, static, asymptotically flat vacuum solutions, and it was also shown that these solutions do not always admit regular and static, static and asymptonically flat solutions.
Abstract: In the general theory of relativity the active mass M of a static source can be written exactly as an integral over a certain linear combination of the diagonal components of the stress-energy tensor. Two corresponding integrals are found within the framework of the Brans-Dicke theory which give the values of those two constants characterizing the source which alone enter into the metric tensor at points sufficiently remote from the source. After dealing with some concomitant results it is shown that the Brans-Dicke equations do not admit everywhere regular, static, asymptotically flat vacuum solutions.