Showing papers in "General Relativity and Gravitation in 1971"
TL;DR: In this article, the exact solution from the Schwarzschild metric was obtained by means of a singular Lorentz transformation, and the result was identical with the exact solutions obtained from the singular Langevin transformation.
Abstract: The gravitational field of a massless point particle is first calculated using the linearized field equations. The result is identical with the exact solution, obtained from the Schwarzschild metric by means of a singular Lorentz transformation. The gravitational field of the particle is nonvanishing only on a plane containing the particle and orthogonal to the direction of motion. On this plane the Riemann tensor has a δ-like singularity and is exactly of Petrov typeN.
595 citations
TL;DR: In this paper, a boundary is attached on which incomplete geodesics terminate as well as inextensible timelike curves of finite length and bounded acceleration, and the construction is free ofad hoc assumptions concerning the topology of the boundary and the identification of curves defining the same boundary point.
Abstract: 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.
221 citations
210 citations
TL;DR: In this paper, it was shown that given a curved space-time with a metric tensorgij, Maxwell's equations may be written as if they were valid in a flat space time in which there is an optical medium with a constitutive equation.
Abstract: Given a curved space-time with a metric tensorgij, Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium with a constitutive equation.
132 citations
75 citations
TL;DR: In this article, a causal boundary is defined by assigning a future and a past endpoint to any non-extensible timelike or null line, and a topology and a partial ordering can be introduced on this boundary.
Abstract: A definition of a causal boundary
$$\dot V$$
is given by assigning a future and a past endpoint to any non-extensible timelike or null line. A topology and a partial ordering can be introduced on
$$\bar V: = \dot V \cup V$$
. The usual conditions for the causal structure can be formulated as properties of
$$\dot V$$
. This boundary is compared with other types of boundaries.
67 citations
56 citations
TL;DR: In this article, some gravitational radiation antenna designs are discussed which are capable of distinguishing between the spin zero scalar radiation predicted by the Brans-Dicke theory of gravitation and the spin two tensor radiation predicted in the Einstein theory of gravity.
Abstract: Some gravitational radiation antenna designs are discussed which are capable of distinguishing between the spin zero scalar radiation predicted by the Brans-Dicke theory of gravitation and the spin two tensor radiation predicted by the Einstein theory of gravitation. The antennas will also give information concerning the direction to the source of radiation, and will measure the polarization of the tensor radiation. The designs consist of symmetric masses with approapriately spaced and oriented transducers. The transducers are combined to give orthogonal outputs. Linear combinations of these orthogonal outputs then are uniquely associated with the various possible combinations of radiation type, propagation, direction and polarization, orientation.
48 citations
TL;DR: In this paper, the problem of non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case.
Abstract: The problem tackled by B. K. Datta, [1] in a recent paper concerning non-static spherically symmetric systems in which the particle motion is, in a certain sense, purely transverse, is further developed and compared with the Newtonian case. A full classification of the possible motions is given.
46 citations
TL;DR: In this paper, the authors have given precise statements of the main principles that underly general relativity, and they have used the original terms, principle of equivalence, etc., to designate the formulations given here primarily for convenience and because they feel that their formulations are, at least in the spirit of the general accepted meaning of these appellations.
Abstract: We have given what, we hope, are precise statements of the main principles that underly general relativity. It is not our intention to argue that these statements correspond to the original statements of these principles. We have used the original terms, principle of equivalence, etc., to designate the formulations given here primarily for convenience and because we feel that our formulations are, at least, in the spirit of the general accepted meaning of these appellations. Our formulation of these principles rests primarily on the observation that there are two types of objects that appear in the descriptions of physical systems, which we have termed absolute and dynamical. A covariance group consists of those transformations which transform one observable set of values of these objects into another observable set and correspond to the passive transformations that one can carry out on the system. An invariance group is the subgroup of a covariance group that leaves invariant the absolute objects. If there are no absolute objects, the two groups coincide. The principle of general covariance asserts that the Einstein group, that is, ‘the group of arbitrary local coordinate transformations’, is a covariance group of all physical systems that can be described by space-time theories. The requirement that the Einstein group is also an invariance group of all physical systems constitutes the principle of general invariance. Support for this latter principle comes first from a Machian type of argument that there should be no absolute objects in nature. A weak form of the principle of equivalence that asserts the equivalence of inertial effects to gravitational effects (but not necessarily conversely) allows one to conclude the impossibility of distinguishing between arbitrary active and passive coordinate transformations. Since the latter transformations constitute the Einstein group, we conclude that the former also constitute this group. Since the active transformations constitute an invariance group, we are again led to the conclusion that the Einstein group is the invariance group, of all spacetime systems.
29 citations
TL;DR: In this paper, the authors consider l'espace muni d a metrique conforme a la metrique quotient and donnons deux arguments en faveur de l'interpretation de la premiere comme metrique d space.
Abstract: Nous rappelons brievement la theorie des espaces-temps stationnaires et celle des espaces metriques. Nous considerons l'espace muni d'une metrique conforme a la metrique quotient et nous donnons deux arguments en faveur de l'interpretation de la premiere comme metrique d'espace. Nous discutons les implications de cette interpretation pour le probleme des sources des solutions statiques de Schwarzschild et Curzon, et nous montrons que ces deux solutions ont une source ponctuelle proportionnelle a la distribution de Dirac.
TL;DR: In the early years of general relativity, it was presumably felt that global questions, while possibly of some physical interest, could safely be deferred until a litter stage as discussed by the authors, and the most pressing questions were local in character, e.g., the suitability of de~'ribing the gra~ itational ticld by a metric, the structure and consequences of Einstein's eqttalions, etc.
Abstract: in the ea:ly years of general relativity, the most pressing questions ~vcre local in character, e.g., the suitability of de~'ribing the gra~ itational ticld by a metric, the structure and consequences of Einstein's eqttalions, etc. It was presumably felt that global questions, while possibly of some physical interest, could safely be deferred until a litter stage. We are now involved in this later stage. Perhaps the most important reason for the rcceilt emphitsis on global properties was tile realization that to establish certain results ~ i n particular, the theorems on singularities ~it is neces,;ary at the outset to exercise some control over the admissible global bchavi()r of the spacetime. The .scope of global work his gradually I~'en extended beyond attempts to control misbehavior until t t~ay global m,:thods comprise a small but vigorous brat.oh of relativity. "What have we gained from these efforts ? We h:|ve becolne nlorc sensitive to glob:d possibilities and pitfalls. (When will a global condition be needed? Which intuitive ideas have been formulalcd precisely? What i, re the consequences of imposing various conditions ? Ilow restrictive are the conditions ?j We hitve reached a lx.ttcr understanding of the various levels of structure of a space-time and their interaction. (Which properties of a .~pacetintc involve only the c:.tusal .,,|ructurc, which only the toi~t~logy, etc. ? Do the causal relations determine the topology?) We have becll led to deeper and more r trealments of kno~.~, n result.,;. (]'lie IIOlit)ll Ol,"l 'generic' property of space-times, for example, offers a potentially v;,luablc approach to singularities.) Finally. ~e h:,ve come to appreciate that the structure of a space-time in tile large may have tme,~pectcd physical signiticante. (I)o the homoh)gy or homot,~py groups, the Siicfcl Whitney cL,sscs, or the spinor structure have implic:ttions for clcmclltary particle physics ?) This pap~;r con,,ists of a collecti,m r162 ;tl~otit the present status of glob;,I work plus ;l fi:w remarks about ~hcre t~c might go from here. (]'he usual caution is in force: many of the impt~rt;mt ildvallccs ill physics have been a result of asking new tlue.~tions which did not appear on ii~ts of
TL;DR: In this article, it is shown 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.
Abstract: 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.
TL;DR: In this paper, it was shown that every Riemannian space admitting a multiply transitive Lie algebra of Killing fields is locally isometric to a homogeneous Riemanian space.
Abstract: The following new results are proved: (1) Every Riemannian space admitting a multiply transitive Lie algebra of Killing fields is locally isometric to a homogeneous Riemannian space. (2) For every closed connceted subgroupH
0 of the invariance group of a non degenerate quadratic form a homogeneous Riemannian space exists whose isotropy group containsH
0. (3) Necessary and sufficient conditions are derived for a Lie algebra
$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{G} $$
to have a realization as multiply transitive Killing fields. These conditions are constructire in the sense that, for a given linear connected isotropy group, Lie algebras
$$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{G} $$
can be calculated algebraically, (4) It is shown how the Riemann tensor of a bomogencous space and its covariant derivatives can be expressed in terms of the metric at one point and the structure constants of the Lie algebra of Killing fields.
TL;DR: In this paper, a pseudo-linear integral representation of the Green's function of the representation in a series of eigenfunctions of an associated linear differential operator is used to find a relation between the multipole moments of field and source in the static case.
Abstract: Multipole moments have already been defined in general relativity independently for both field and source, but owing to the non-linearity of the theory these two concepts have not hitherto been related. Recently Sciama, Waylen and Gilman have found a pseudo-linear integral representation of Einstein's field equations. This representation is here used to find a relation between the multipole moments of field and source in the static case. The technique is to expand the Green's function of the representation in a series of eigenfunctions of an associated linear differential operator.
TL;DR: In this paper, it was shown that for a spherically symmetric perfect fluid solution to be of class one, either (i) e = 0, or (ii) e+R=0,e andR being respectively the eigenvalue of the Weyl tensor in Petrov's classification and spur of the Ricci tensor.
Abstract: It is shown that for a spherically symmetric perfect fluid solution to be of class one, either (i) e=0, or (ii) e+R=0,e andR being respectively the eigenvalue of the Weyl tensor in Petrov's classification and spur of the Ricci tensor. Hence, it is deduced that whereas every conformally flat perfect fluid solution is of class one, the converse is not true in general. However, the converse does hold for all solutions withρ=3p.
TL;DR: Relativite restreinte and relativite generale se referent essentiellement a la geometrie differentielle hyperbolique as discussed by the authors, a notion d'espace fibre differentiable, which domine depuis 1940 toute the geometriques differentialle.
Abstract: Relativite restreinte et relativite generale se referent essentiellement a la geometrie differentielle hyperbolique. Or c'est la notion d'espace fibre differentiable qui domine depuis 1940 toute la geometrie differentielle. C'est pourquoi mathematiciens et physiciens ont pris conscience, depuis longtemps deja, du fait que les espaces fibres constituent un cadre de pensee fondamental pour la relativite, comme ils le font d'ailleurs aussi pour la mecanique analytique classique. Les identifications, parfois abusives, a laquelle se prete la relativite restreinte ne doivent pas masquer cette realite. En introduction au seminaire, le but de cette conference est seulement de rappeler les elements principaux de ce cadre, sans viser a l'originalite sauf sur quelques points.
TL;DR: In this article, the balanced field equations of general relativity have been used for presenting a model for a sphere of charged dust having different densities of matter and charge, and the particular case of the solution arrived at herein.
Abstract: The balanced field equations [1] of general relativity have been used for presenting a model for a sphere of charged dust having different densities of matter and charge. The Schwarzschild's and Penney's solutions are the particular case of the solution arrived at herein. Further equations are solved to get a model in which gravitational attraction and electrical repulsion balance each other.
TL;DR: In this paper, the equivalence of the Euclidean and the Lorentz-covariant representations of the physical laws of the metric tetradrithm has been established.
Abstract: We define a derivation operation working on hybrid objects which are tensors under theEinstein group of coordinate transformations and under theLorentz group of transformations of reference systems. With these general covariant derivations we formulate the principle of the equivalence of theEinstein- and of theLorentz-covariant representations of the physical laws. This principle means the general covariant constance of the metric tetradsh
i
A
(Weyl's lemma).
TL;DR: In a closed universe, every physical system has a discrete infra-structure consisting of closely spaced (ΔE∼h 2/2mR2) energy eigen states.
Abstract: In a closed universe, every physical system has a discrete infra-structure consisting of closely spaced (ΔE∼h
2/2mR2) energy eigen states. Basic physical principles such as the uncertainty relation as well as semi-empirical facts like the finiteness of the world age seem to exclude a detection of this structure.
TL;DR: In this article, a simple example of a multiply-connected, or "v, ormhole" topology trapping electric lines of force was examined, where the interiors of two solid spheres of equal radius are removed from an ordinary three dimensional Euclidean space, and the appropriate points On the surfaces of the two spheres are identified, they obtain a wormhole in our space.
Abstract: in 1956, J. A. Wheeler and C. W. Misner [I] showed in some detail that the existence of charges in the world need not be associated with sources in the electromagnetic field equations, but rather could be described as a consequence of Maxwell's free field equations (i.e. Ffj,,:~,l =0 and F~'";,--0) in a space with a multiply connected topology [2]. The electric lines of force can be ' tra?ped' in the topological structure of space, with the number of trapped lines of force being directly proportional to the charge associated with that field. To make this idea clearer, let us examine a simple example of a multiply connected, or 'v, ormhole' topology trapping electric lines of force. If the interiors of two solid spheres of equal radius are removed from an ordinary three dimensional Euclidean space, and' the appropriate points On the surfaces of the two spheres are identified, we obtain a "wormhole' in our space. If now we imagine that the t**o spheres had been conducting, one having charge q and the other charge q . and that the resultant electric field were fixed during the above reconstruction of our space, we discover that the resultant electric field everywhere obeys the free field equations. However, for an)'one located outside the cutaway portions of the space, there wouk! be no way of telling that the charges were no longer there. For example, integrating the field over any closed surface surrounding one of the wormhole mouths would tell him that the surface still enclosed a charge q. We have created, in Wheeler's words, 'charge without charge'. Due to the symmetry in Maxwell's equations between E and B, magnetic lines of force could similarly be trapped by the topology, creating magnetic charges, ilowever, these have never been observed in nature [3l. Wc theretore make the natural assumption that magnetic lines of force cannot be trapped in a multiply-connected topology. The above concepts can bc put into a rigorous mathematical form [4]. The electromagnetic tensors/-'*~ and ~,,~,~,f'p" are curl free antisymmetric I~ensors, and as such coffespond to closed differential 2+formsfand *f(i.e
TL;DR: In this paper, the scattering of unpolarized Fermions and scalar mesons by single graviton exchange is considered by means of a Feynman graph type perturbation theory scheme.
Abstract: The scattering of unpolarized Fermions and scalar mesons by single graviton exchange is considered by means of a Feynman graph type perturbation theory scheme. In the limit of scattering of the Fermions by very heavy mesons, one obtains the cross section for Fermions scattering in a Schwarzschild metric. The result obtained conflicts with an earlier result of Mitskevich. In the limit of scattering of massless Fermions (neutrinos) with massless scalar mesons it is seen, using Weinberg's treatment of soft graviton Bremsstrahlung, that the cosmological red shift of light cannot be explained by interactions of the light with intergalactic neutrinos.
TL;DR: In this article, the general non-static axially symmetric line element has been considered in the context of Petrov Classification and the space-time is found to be of various Petrov Types under different circumstances.
Abstract: In this paper the general non-static axially symmetric line element has been considered in the context of Petrov Classification. The space-time is found to be of various Petrov Types under different circumstances. The necessary algebraic conditions for such a space-time to be of class one have also been derived. It is found that there exists only one solution representing a plane symmetric class-one null-electromagnetic field.
TL;DR: In this paper, the meson-gravitational field interaction was studied in order to compare quantum and classical results, and it was found that the differential cross section and energy loss agree with the classical results for a low energy meson.
Abstract: The quantum mechanical analog of the problem of a charged particle falling in a gravitational field is studied in order to compare quantum and classical results. The interaction considered is that between a charged scalar meson and an external gravitational field resulting in the emission of a photon. It is found that the differential cross section and energy loss agree with the classical results for a low energy meson. A brief discussion of radiative corrections to the meson-gravitational field interaction is given in order to point out a difficulty which apparently arises when the cut-off method of handling divergent integrals is used.
TL;DR: In this paper, it was shown that a large class of conformal transformations of the metric tensor on a 3D hypersurface leads to sandwich problems that result in elliptic differential equations for the unknown variables.
Abstract: It is shown that a large class of conformal transformations of the metric tensor on a three-dimensional space-like hypersurface leads to sandwich problems that result in elliptic differential equations for the unknown variables.