Showing papers in "General Relativity and Gravitation in 1978"

Classical Gravity with Higher Derivatives

Abstract: Inclusion of the four-derivative terms ∫RμνRμν(−g)1/2 and ∫R2(−g)1/2 into the gravitational action gives a class of effectively multimass models of gravity. In addition to the usual massless excitations of the field, there are now, for general amounts of the two new terms, massive spin-two and massive scalar excitations, with a total of eight degrees of freedom. The massive spin-two part of the field has negative energy. Specific ratios of the two new terms give models with either the massive tensor or the massive scalar missing, with correspondingly fewer degrees of freedom. The static, linearized solutions of the field equations are combinations of Newtonian and Yukawa potentials. Owing to the Yukawa form of the corrections, observational evidence sets only very weak restrictions on the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The dynamical content of the linearized field is analyzed by reducing the fourth-order field equations to separated second-order equations, related by coupling to external sources in a fixed ratio. This analysis is carried out into the various helicity components using the transverse-traceless decomposition of the metric.

Metric-affine variational principles in general relativity. I. Riemannian space-time

Abstract: Within the confines of conventional general relativity, variational principles are analyzed in which the metric tensor and the asymmetric linear connection are varied independently. The constraint that space-time remain Riemannian is introduced by means of the Lagrange multiplier technique. The Lagrange multiplier which effects this constraint, the hypermomentum current, is closely related to the constraint “force” which keeps space-time Riemannian and should be a measure for the violation of the Riemannian constraint at the microscopic level.

On a new variational principle in general relativity and the energy of the gravitational field.

Abstract: A new variational principle based on the affine connection in space-time is proposed. This leads to a new formulation of general relativity. The gravitational field is a field of inertial frames in space-time. The metricg appears as a momentum canonically conjugate to the gravitational field. In the case of simple matter fields, e.g., scalar fields, electromagnetic fields, Proca fields, or hydrodynamical matter, the new formulation is equivalent to the traditional one. A new formulation of conservation laws is proposed.

Sources for the Reissner-Nordstrom metric

Abstract: New, physically motivated static sources for the Reissner-Nordstrom metric are found. One is a generalization of the Schwarzschild interior solution representing a sphere of constant nongravitational energy density. The other is a family of solutions for which the mass is electromagnetic in origin. Some general results are found. For a charged fluid sphere in equilibrium with pressure,m2 >q2. For a charged body with equation of state ρ=ρ (p), where ρ(0)=0, the body is under tension at every point when the charge density has the same sign throughout.

Friedmann-like cosmological models without singularity

Abstract: The Einstein-Cartan theory of gravitation (“general relativity with spin”) provides a specific spin-spin contact interaction of matter, in addition to the usual long-range gravity. This new interaction enables us to prevent singularities in Cosmological models. It is shown how this mechanism works in the case when the standard Einstein-Cartan equations are valid at a microphysical level, and some spin-spin terms remain from the averaging procedure for randomly distributed spins. In contrast with the case of aligned spin distributions, it is possible to take over the isotropic and spatially homogeneous (i.e., Friedmannian) models into the Einstein-Cartan theory. These models can be made free from singularity, thanks to the self-interaction of spinning fluid.

The dynamics of polarization

Abstract: Long-standing problems concerning the structure of the energy-momentum tensor and the thermodynamics of a polarized medium are reexamined in the light of an exact, fully relativistic kinetic model.

Thermodynamic equilibrium of a gravitating sphere in Lyra's geometry

Abstract: This paper deals with a particular case of Lyra's modification of Riemannian geometry in which the consequences of the thermodynamic equilibrium of a gravitating fluid sphere have been considered. These considerations lead to a zero red shift in this static model.

Quantum mechanics of electromagnetically bounded spin- 1 / 2 particles in an expanding universe: I. Influence of the expansion.

Abstract: The quantum mechanically described electron in an external electromagnetic field, both embedded in an expanding universe with shear, is discussed. This is important for the fundamental question if a quantum mechanically treated atomic clock in curved space-time (based on a hydrogen atom) shows proper or gravitational time. Furthermore, contradictory results reported by other authors seem to imply that quantum mechanics cannot be reconciled with curved space-time. It is shown that this is not the case for expanding Robertson-Walker universes. As basis, in this paper a Hilbert space formulation of the problem with special regard to the Hamiltonian is given. The respective influence of the cosmic expansion and the intrinsic and extrinsic curvatures of the cosmic hypersurfaces on bound quantum mechanical systems is treated in general. For the special case of an expanding 3-flat (e=0) Robertson-Walker universe it is shown that the energy levels of a hydrogen atom agree completely with the one in 4-flat space-time, so that in this case the hydrogen atom can be taken as atomic clock showing proper time.

Bimetric gravitation theory on a cosmological basis.

Abstract: In the bimetric theory of gravitation the background metric tensor γ μν , previously taken as describing flat space-time, is now chosen on the basis of a model of the universe. In accordance with the perfect cosmological principle, it is taken as describing a space-time of constant curvature. There are three possible forms, corresponding tok=0, 1, −1. Only fork=1 (a closed universe) does the model not go through a singular state; hence this is the appropriate choice. The isotropic solution of the field equations can be chosen to agree with the present cosmological observations. For small systems like the solar system the theory gives the same results as before, in agreement with those of general relativity.

A note on Killing tensors

Abstract: The connection between symmetric and skew-symmetric Killing tensors is studied. Some theorems on skew-symmetric Killing tensors are generalized, and it is shown that in all type-D vacuum metrics admitting a symmetric Killing tensor, this Killing tensor can be given in terms of a skew-symmetric Killing tensor.

Quantum mechanics of electromagnetically bounded spin-1/2 particles in expanding universes: II. Energy spectrum of the hydrogen atom

Abstract: Completing the preceding paper, the energy spectrum of the hydrogen atom in expanding Robertson-Walker universes is studied in detail using rigorous methods of functional analysis. Thereby, for closed universes (spherical case,e=1), the corresponding electromagnetic field needs special considerations. For the hyperbolic case (e=−1) it is shown (a) that the Hamilton operator is uniquely self-adjoint, (b) that the continuous energy spectrum agrees with the one in 4-flat space-time and that the energy eigenvalues are bounded by±m 0 , (c) that they approach Minkowski space spectrum for increasing curvature radius, and (d) that the hydrogen atom cannot be used as an atomic clock showing proper time. For the spherical case (e=1) it is shown (a) that the Hamilton operator is uniquely self-adjoint and (b) that the energy spectrum is solely discrete.

On geometrodynamics with tetrad fields

Abstract: In this paper, we extend Kuchař's analysis [1] to geometrodynamics driven by sources of arbitrary spin: starting from a given matter action added to ADM's gravitational action, we derive the corresponding Hamiltonian. We next calculate the strong value of the Poisson brackets of the constraints. Our general derivation leads to Deser-Isham [9] and Dirac's results [4] when applied to the particular cases of pure geometrodynamics and geometrodynamics with a spin-1/2 field.

A note on Godel's metric

Abstract: It is proved that every line element of the formds2=−dt2=−dx2+dy2+D(x)dz2-2E(x)dzdt, which satisfies Einstein equations for a perfect fluid, is necessarily isometric to the Godel's universe.

The nonlinear graviton in interaction with a photon

Abstract: It is shown that Einstein-Maxwell complex space-times with self-(anti-self-) dual Weyl tensor and algebraically general anti-self-(self-) dual Maxwell tensor are completely characterized as quasi-Kahlerian space-times with vanishing scalar curvature. Following Penrose's interpretation ofH-spaces, we propose that an “electrifiedH-space” be interpreted as a nonlinear graviton in interaction with a photon. Two families of exact solutions are presented as examples.

A new Lagrangian for the vacuum einstein equations and its tetrad form

Abstract: We give a modification of the Palatini Lagrangian for the free gravitational field that yields the vanishing of the torsion as a result of the field equations and requires only the assumption of the symmetry of the metric. We transcribe this Lagrangian into the tetrad formalism and show how the tetrad form of the Einstein field equations follows from it. Some remarks on possible generalization to a theory with nonvanishing torsion in the presence of matter conclude the paper.

“Conserved” quantities for isolated gravitational systems

Abstract: This paper implements an idea suggested by Penrose and MacCallum. Starting from the twistor equation for a symmetric two-index spinor, it provides a derivation of expressions for energy momentum and angular momentum of an isolated gravitational system at future null infinity in general relativity. The approach employed here is rather straightforward and is related to symmetries in a convincing way.

Twistor surfaces and right-flat spaces

Abstract: The connection between the deformed twistor space of Penrose and Plebanski's form for the general right-flat metric is explored. A Hamiltonian formalism for obtaining the twistor surfaces in a right-flat space with Plebanski's Ω-function as Hamiltonian is obtained.

Time Machine and Geodesic Motion in Kerr Metric

Abstract: The existence of nontrivial causality violation is a peculiar property of the space-time around a naked singularity. In the case of Kerr metric witha > m we have found that for a particular class of geodesies that could in principle violate causality, the conditions for causality violation are never satisfied.

Static and stationary axially symmetric gravitational fields of bounded sources. I. Solutions obtainable from the van Stockum metric

Abstract: This paper shows that a new class of axially symmetric static electrovacuum solutions and the Kerr solution are obtainable from the van Stockum metric. The new class contains an infinite set of asymptotically flat solutions (in closed form), each of which involves an arbitrary set of parameters. The parameters have to be interpreted as functions of massm, chargee, and higher electric multipole momentsα i of the particle. The casee=α i =0 leads to the Darmois metric. Well-known and new examples are given.

Equivalence of Vacuum Yang-Mills Gravitation and Vacuum Einstein Gravitation

Abstract: In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are ζRκα +CκρασRρσ = 0 and and\(\triangledown _{\left[ {\kappa ^R \lambda } \right]v} = 0\). HereR κα is the Ricci curvature andCμκαν is the Weyl conformal curvature; ξ is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsRκα = 0. The proof uses the Newman-Penrose formalism.

Spatially homothetic cosmological models

Abstract: Spatially homothetic cosmological models are defined as space-time manifolds acted on by a 3-parameter group of transformations transitive over spacelike hypersurfaces, whose effect is to multiply the metric by a constant conformal factor Previous work on these models is reviewed briefly and the algebraic classification scheme of Eardley is described Explicit forms of the metric and group generators are given for each class in terms of a conformally synchronous coordinate system using an invariant orthogonal basis of 1-forms It is shown that certain subclasses are necessarily incomplete in the sense that a singularity of the conformally synchronous system must develop within a finite time

Vortical null orbits, repulsive barriers, energy confinement in Kerr metric

Abstract: We give the complete analytical description of the null trajectories in the field of a Kerr naked singularity. Two peculiar phenomena are described: the existence of repulsive barbiers in ther < 0 world and the existence of null circular bound orbits which surround the singularity in “shells.” They distribute around the surface atr = m, which is the position of the horizon in the extreme black-hole case; this suggests that a naked singularity “remembers” the position of the last horizon.

Spin precession in the relativistic two-body problem.

Abstract: Synge's approximation procedure is applied to calculate the spin precession of either body in a binary system consisting of two rotating, spherical, rigid bodies of comparable mass and radius. The calculations are valid for the case in which the mass-radius ratio of each body, as well as the ratio of the radius of either body to the distance between their centers, is small. The results agree with those of earlier authors, who use different techniques, except for a term that arises from the effect of the rotation on the stress within the bodies. This term is similar in form to the quadrupole term of Barker and O'Connell, which they obtain when they allow the bodies to become distorted under the influence of the rotation.

Is the universe expanding

Abstract: It is shown that spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes, if the usual assumptions are made about the local physical laws determining the behavior of matter, provided that the universe is inhomogeneous and our galaxy is situated close to one of its centers. Only (i) unverifiable a priori assumptions, (ii) detailed physical and astrophysical arguments, or (iii) observation of the time variation of cosmological quantities can lead us to conclude that the universe we live in is not such a static space-time.

Relativistic equations of motion of extended bodies

Abstract: We derive the most general equations of motion in the post-Newtonian approximation of general relativity for a bounded system of extended bodies with arbitrary internal structure and internal motions, and we explore in detail the conditions under which the motion of the bodies deviates from the geodesic motion.

Exact cosmological solution with particle creation in JBD theory

Abstract: Exact solutions are sought by taking the generated particles of spin 1/2 (according to the creation rate of Schafer and Dehnen [1]) as matter sources of the Cosmological equations of JBD theory. There exists one exact solution for which the “gravitational constant” decreases linearly with time and the mass of the universe increases proportionally to the square of its age (Dirac's hypotheses). The radius of curvature increases linearly with time while the density decreases inversely with it. It is found that for an age of the universe ≃ 10−22 sec only two particles have populated the universe. This is assumed to be the initial state of the model. The calculated present particle number and their density are in agreement with the observed data. This model implies that all present matter (excluding the two initial particles) has been created by the expansion of the universe.

Monad method and canonical formalism of general relativity

Abstract: In this note the general monad method is systematically represented, and it is shown how it may be reduced to its two basic special gauges. The last section deals with two kinds of canonical formalism, “coordinate” and “referential” ones, based on the kinemetric gauge.

Domains of stationary communications in space-time

Abstract: Basic relationships between the causal connectivity properties and the symmetry group invariance properties of space-time manifolds are discussed with a view to applications in the theory of stationary black holes. In particular the results given here provide a rigorous justification for the application of Israel's theorem [6] to static black holes as strictly defined; they also provide an essential step in the proof of the “no-hair” theorem for stationary-axisymmetric pure vacuum black holes as described by Carter [29] and extended by Robinson [10]. One of the main results is the demonstration that if the causality axiom holds, the domain of communications of any stationary domain has the form of a fiber bundle over a well-behaved base manifold and that if also the invariance group is orthogonally transitive and the stationary domain is simply connected, then the domain of communication coincides with the stationary domain, so that the correspondingglobally defined horizons coincide with the relevantlocal isometry or Killing horizons.

Einstein-Maxwell space-times with symmetries and with non-null electromagnetic fields

Abstract: General properties of solutions (g, F) of the Einstein-Maxwell field equations are discussed, whereg is a metric tensor andF is a non-null Maxwell field. In particular the case is discussed whereg admits a Killing vector fieldv with special emphasis on the case wherev is not admitted byF, i.e., the electromagnetic field does not have a symmetry of the metric tensor. An example is given of a solution (g, F) in whichg admits a hypersurface orthogonal Killing vector not admitted byF.

A maximally symmetric space with torsion

Abstract: A maximally symmetric space, i.e., homogeneous and isotropic at every point, possessing totally antisymmetric torsion is dealt with. It is found that maximum symmetry restricts the dimension of the space to three. The three-curvature tensor for the space is obtained and from its form a three-metric is then constructed. The three-space is then allowed to evolve in time so that a four-metric of the formds 2= −dt 2+ (3)g ij dx i dx j is possible. From this an equation of motion is obtained which predicts an initial- and final-state singularity.