Showing papers on "Introduction to the mathematics of general relativity published in 1969"
TL;DR: In this paper, it was shown that given any set of initial data for Einstein's equations which satisfy the constraint conditions, there exists a development of that data which is maximal in the sense that it is an extension of every other development.
Abstract: It is shown that, given any set of initial data for Einstein's equations which satisfy the constraint conditions, there exists a development of that data which is maximal in the sense that it is an extension of every other development These maximal developments form a well-defined class of solutions of Einstein's equations Any solution of Einstein's equations which has a Cauchy surface may be embedded in exactly one such maximal development
578 citations
TL;DR: Algebraically degenerate solutions of the Einstein and Einstein-Maxwell equations are studied in this article, where explicit solutions are obtained which contain two arbitrary functions of a complex variable, one function being associated with the gravitational field and the other mainly with the electromagnetic field.
Abstract: Algebraically degenerate solutions of the Einstein and Einstein‐Maxwell equations are studied Explicit solutions are obtained which contain two arbitrary functions of a complex variable, one function being associated with the gravitational field and the other mainly with the electromagnetic field
373 citations
Book•
01 Jan 1969
TL;DR: In this paper, the authors present a model of the Lorentz transformation and its relation to general relativistic physics, including the relation between acceleration and gravity, as well as its relation with the equivalence principle of the Mach's Principle.
Abstract: 1 The Rise and Fall of Absolute Space.- 1.1 Definition of Relativity.- 1.2 Newton's Laws.- 1.3 The Galilean Transformation.- 1.4 The Set of All Inertial Frames.- 1.5 Newtonian Relativity.- 1.6 Newton's Absolute Space.- 1.7 Objections to Newton's Absolute Space.- 1.8 Maxwell's Ether.- 1.9 Where is Maxwell's Ether?.- 1.10 Lorentz's Ether Theory.- 1.11 The Relativity Principle.- 1.12 Arguments for the Relativity Principle.- 1.13 Maxwellian Relativity.- 1.14 Origins of General Relativity.- 1.15 Mach's Principle.- 1.16 Consequences of Mach's Principle.- 1.17 Cosmology.- 1.18 Inertial and Gravitational Mass.- 1.19 The Equivalence Principle.- 1.20 The Semistrong Equivalence Principle.- 1.21 Consequences of the Equivalence Principle.- 2 Einsteinian Kinematics.- 2.1 Basic Features of Special Relativity.- 2.2 On the Nature of Physical Laws.- 2.3 An Archetypal Relativistic Argument.- 2.4 The Relativity of Simultaneity.- 2.5 The Coordinate Lattice.- 2.6 The Lorentz Transformation.- 2.7 Properties of the Lorentz Transformation.- 2.8 Hyperbolic Forms of the Lorentz Transformation.- 2.9 Graphical Representation of the Lorentz Transformation.- 2.10 World-picture and World-map.- 2.11 Length Contraction.- 2.12 Length Contraction Paradoxes.- 2.13 Time Dilation.- 2.14 The Twin Paradox.- 2.15 Velocity Transformation.- 2.16 Proper Acceleration.- 2.17 Special Relativity without the Second Postulate.- 3 Einsteinian Optics.- 3.1 The Drag Effect.- 3.2 The Doppler Effect.- 3.3 Aberration and the Visual Appearance of Moving Objects.- 4 Spacetime and Four-Vectors.- 4.1 Spacetime.- 4.2 Three-Vectors.- 4.3 Four-Vectors.- 4.4 Four-Tensors.- 4.5 The Three-Dimensional Minkowski Diagram.- 4.6 Wave Motion.- 5 Relativistic Particle Mechanics.- 5.1 Domain of Sufficient Validity of Newton's Laws.- 5.2 Why Gravity Does not Fit Naturally into Special Relativity.- 5.3 Relativistic Inertial Mass.- 5.4 Four-Vector Formulation of Relativistic Mechanics.- 5.5 A Note on Galilean Four-Vectors.- 5.6 Equivalence of Mass and Energy.- 5.7 The Center of Momentum Frame.- 5.8 Relativistic Billiards.- 5.9 Threshold Energies.- 5.10 Three-Force and Four-Force.- 5.11 De Broglie Waves.- 5.12 Photons. The Compton Effect.- 5.13 The Energy Tensor of Dust.- 6 Relativity and Electrodynamics.- 6.1 Transformation of the Field Vectors.- 6.2 Magnetic Deflection of Charged Particles.- 6.3 The Field of a Uniformly Moving Charge.- 6.4 The Field of an Infinite Straight Current.- 7 Basic Ideas of General Relativity.- 7.1 Curved Surfaces.- 7.2 Curved Spaces of Higher Dimensions.- 7.3 Riemannian Spaces.- 7.4 A Plan for General Relativity.- 7.5 The Gravitational Doppler Effect.- 7.6 Metric of Static Fields.- 7.7 Geodesics in Static Fields.- 8 Formal Development of General Relativity.- 8.1 Tensors in General Relativity.- 8.2 The Vacuum Field Equations of General Relativity.- 8.3 The Schwarzschild Solution.- 8.4 Rays and Orbits in Schwarzschild Space.- 8.5 The Schwarzschild Horizon, Gravitational Collapse, and Black Holes.- 8.6 Kruskal Space and the Uniform Acceleration Field.- 8.7 A General-Relativistic "Proof" of E = mc2.- 8.8 A Plane-Fronted Gravity Wave.- 8.9 The Laws of Physics in Curved Spacetime.- 8.10 The Field Equations in the Presence of Matter.- 8.11 From Modified Schwarzschild to de Sitter Space.- 8.12 The Linear Approximation to GR.- 9 Cosmology.- 9.1 The Basic Facts.- 9.2 Apparent Difficulties of Prerelativistic Cosmology.- 9.3 Cosmological Relativity: The Cosmological Principle.- 9.4 Milne's Model.- 9.5 The Robertson-Walker Metric.- 9.6 Rubber Models, Red Shifts, and Horizons.- 9.7 Comparison with Observation.- 9.8 Cosmic Dynamics According to Pseudo-Newtonian Theory.- 9.9 Cosmic Dynamics According to General Relativity.- 9.10 The Friedmann Models.- 9.11 Once Again, Comparison with Observation.- 9.12 Mach's Principle Reexamined.- Appendices.- Appendix I: Curvature Tensor Components for the Diagonal Metric.- Appendix II: How to "Invent" Maxwell's Theory.- Exercises.
188 citations
01 Jul 1969
TL;DR: The NUT metric is interpreted as the field of (a) a mass around the origin of coordinates, and (b) a semi-infinite massless source of angular momentum as discussed by the authors.
Abstract: The NUT metric is interpreted as the field of (a) a mass around the origin of coordinates, and (b) a semi-infinite massless source of angular momentum.
151 citations
TL;DR: In this paper, the well known method ofNewman andPenrose is used to find solutions of the Einstein empty space field equations, which are algebraically special and where the degenerate principal null vectors are not hypersurface orthogonal.
Abstract: The well known method ofNewman andPenrose is used to find solutions of the Einstein empty space field equations, which are algebraically special and where the degenerate principal null vectors are not hypersurface orthogonal. As is to be expected the method systematically yields the results obtained byKerr. An explanation is given of the complex coordinate transformation technique of generating new metrics from Schwarzschild's; also a generalisation of Kerr and Schild type metrics is investigated.
95 citations
TL;DR: In this article, simple solutions of the Einstein scalar and Brans-Dicke field equations are exhibited, and the nature of the Killing horizons of some static solutions is discussed.
Abstract: Simple solutions of the Einstein scalar and Brans-Dicke field equations are exhibited, and the nature of the Killing horizons of some static solutions is discussed.
91 citations
TL;DR: In this article, a generalization of Bornfeld nonlinear electrodynamics, due to Plebanski, is reformulated in the context of general relativity theory, and a class of nonsingular, static, spherically symmetric solutions of the modified Einstein-Maxwell equations are given, corresponding to a point-charge source.
Abstract: A generalization of Born‐Infeld nonlinear electrodynamics, due to Plebanski, is reformulated in the context of general relativity theory. A class of nonsingular, static, spherically symmetric solutions of the modified Einstein—Maxwell equations are given, corresponding to a point‐charge source. The metric tensors of these solutions are shown to approach the Riesner‐Nordstrom metric tensor at large distances from the source, if one makes the proper identification of mass.
66 citations
TL;DR: In this article, the system of coupled differential equations to which the constraints on the Cauchy data reduce if expressed in terms of the shift vector Nk and the lapse N0 was examined.
Abstract: We examine the system of coupled differential equations to which the constraints on the Cauchy data reduce if expressed in terms of the ``shift'' vector Nk and ``lapse'' N0. If (3)gij and ∂ (3)gij/∂t are given and Dirichlet boundary conditions are imposed, the solution Nk is found to be unique if 2 × (energy density) − (three‐curvature) > 0, but need not be unique when this inequality is not satisfied. No general existence theorem is known, but we list some conditions which make solutions impossible.
55 citations
51 citations
41 citations
TL;DR: In this article, a general equation for the rate of change of the total energy of a sphere in a spherically symmetric distribution of charged matter is derived for the case of a spheroid.
Abstract: The Einstein–Maxwell equations for a spherically symmetric distribution of charged matter are studied. A general equation is derived for the rate of change of the "total energy" of the sphere in te...
TL;DR: In this paper, the field equations for coupled gravitational and zero-mass scalar fields in the presence of a point charge were solved in the spherically symmetric static case.
Abstract: The field equations for coupled gravitational and zero-mass scalar fields in the presence of a point charge are solved in the spherically symmetric static case. The resulting solution is the generalization of the Reissner-Nordstr\"om solution in the presence of a zero-mass meson field.
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TL;DR: Bilaniuk and Sudarshan as discussed by the authors argued that valid solutions of Albert Einstein's relativity equations describe faster-than-light particles called "tachyons" and that tachyons must exist.
Abstract: “Anything that is not forbidden is compulsory,” says Murray Gell-Mann's half-facetious totalitarian principle. What then about faster-than-light particles called “tachyons”? In their May article Olexa-Myron Bilaniuk and E. C. George Sudarshan argued that valid solutions of Albert Einstein's relativity equations describe such particles. Thus if Einstein's equations are accurate descriptions of the physical universe and if solutions not forbidden are compulsory, tachyons must exist.
TL;DR: An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner-Nordstrom metri... as mentioned in this paper.
Abstract: An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordstrom metri...
TL;DR: A reasonable course of investigation in fundamental physics should fully exploit Einstein's approach to the meaning of space-time; it would proceed by exploring, in a unified way, the predictions of generalized equations of general relativity that would encompass in one formalism all of the domains of interaction as mentioned in this paper.
Abstract: A REASONABLE COURSE of investigation in fundamental physics should fully exploit Einstein's approach to the meaning of space—time; it would proceed by exploring, in a unified way, the predictions of generalized equations of general relativity that would encompass in one formalism all of the domains of interaction—from fermis to light years.
Journal Article•
TL;DR: A general solution of the field equations of general relativity theory has been obtained for a composite sphere having a number of shells, one above the other, of different densities as mentioned in this paper, which is a special case of the case described in this paper.
Abstract: A general solution of the field equations of general relativity theory has been obtained for a composite sphere having a number of shells, one above the other, of different densities.
TL;DR: A tetrad formulation of the conservation-law generator of general relativity is presented in this paper, which has the expected tensor character and appropriately reduces to Moller's tetrad superpotential.
Abstract: A tetrad formulation of the conservation-law generator of general relativity is presented. This expression has the expected tensor character and appropriately reduces to Moller’s tetrad superpotential. Use of this expression in the explicit formulation of the actual conservation laws admitted requires considerations of the symmetry properties, if any, of the given space-time. The intrinsic form of the conservation-law generator, which is fundamental to local applications of the conservation laws, is given. Also, several alternative tetrad formulations of « conservation-law generators » are briefly considered.
TL;DR: In this article, it was shown that, also in the mixed initial and boundary value problem, Einstein's equations may be replaced by two subsystemsT /m=0 and T /m = 0, provided that the initial data verify the consistency conditions and that the analogous relations are imposed on the boundaries of the given domain.
Abstract: It is shown that, also in the mixed initial and boundary value problem, Einstein's equations may be replaced by the two subsystemsT
/m=0 and
, provided that the initial data verify the consistency conditions
and that the analogous relations
are imposed on the boundaries of the given domain.
TL;DR: In this article, it was shown that the covariant formulation of electrodynamics in General Relativity is incompatible with the Einstein principle of equivalence for the case of a resistanceless current-carrying wire in a static spherically symmetric gravitational field.
Abstract: It is shown that the customary covariant formulation of electrodynamics in General Relativity is incompatible with the Einstein Principle of Equivalence. This is demonstrated for the case of a resistanceless current-carrying wire in a static spherically symmetric gravitational field—where the Einstein Principle of Equivalence implies the existence, in the vicinity of the wire, of a non-zero component of the electric field parallel to the wire, whereas the covariant form of Maxwell's equations does not. An experiment, involving a superconducting current-carrying wire segment placed in the Earth's gravitational field, is suggested. Whether or not a component of electric field parallel to the wire, at a point in the wire's vicinity, would be detected would resolve the issue.
TL;DR: In this paper, the authors extended the Bondi-Sachs analysis of empty-space gravitational Gelds to include the presence of a pure-radiation stress energy tensor.
Abstract: The Bondi-Sachs analysis of empty-space gravitational Gelds is extended to include the presence of a pure-radiation stress-energy tensor, T„,=crk„k„. A pure-radiation news function is defined and shown to contribute to the change of the mass aspect in a way analogous to the gravitational news functions. It is suggested that this type of analysis may prove useful in the study of bodies simultaneously emitting highfrequency incoherent and low-frequency coherent gravitational radiation.
TL;DR: In this article, a summary of the Lorentz principle applied to general relativity is given, along with a notation for the Christoffel symbols and the Riemann-Christoffel tensor.
Abstract: In a number of publications dealing with the Lorentz principle applied to general relativity we have introduced step by step a notation which is particularly useful to reflect our own physical ideas. In the present paper we give a summary of this notation and the involved technique. We have freed the formalism of a number of minor inconsistencies to be found in the earlier works and show how with the help of this formalism simple expressions can be derived — among others — for the Christoffel symbols and the Riemann—Christoffel tensor.
TL;DR: In this article, conditions which must be satisfied by the energy-momentum tensor of the null electromagnetic field (i.e., by a field of pure radiation) in the general theory of relativity are formulated within the framework of the Newman-Penrose formalism.
Abstract: Conditions which must be satisfied by the energy-momentum tensor of the null electromagnetic field (i.e., by a field of pure radiation) in the general theory of relativity are formulated within the framework of the Newman-Penrose formalism. If a normal geodesic congruence is permitted in the space (this is equivalent to the allowed existence of wave fronts), there can be only two types of null electromagnetic fields. The asymptotic behavior of one of these types is analyzed.