Showing papers in "Classical and Quantum Gravity in 1986"
TL;DR: Christodoulou's recent analysis of naked singularities in time-symmetric Tolman-Bondi collapse is simplified and generalised to a wider class of models as discussed by the authors.
Abstract: Christodoulou's recent analysis (1984) of naked singularities in time-symmetric Tolman-Bondi collapse is simplified and generalised to a wider class of Tolman-Bondi models. The strengths of the naked singularities are assessed in terms of limiting focusing conditions.
206 citations
TL;DR: In this article, it was shown that the conformal motions of the Robertson-Walker spacetimes do not map a fluid flow conformally to the homogeneous hypersurfaces.
Abstract: It is well known that Robertson-Walker spacetimes admit a conformal Killing vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing the authors to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. They also use these non-normal vectors to find the general solution of the null geodesic equation and photon Liouville equation.
123 citations
TL;DR: In this paper, it is proved that a weakly asymptotically simple and empty spacetime must be future-asymptotic predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface.
Abstract: An attempt is made to formulate the cosmic censorship hypotheses put forward by Penrose (1979) as a theorem which could be subject to a mathematical proof. It is proved that a weakly asymptotically simple and empty spacetime must be future asymptotically predictable if the energy and the strong causality conditions hold and either all singularities are of Tipler's strong curvature type and once singularity occurs there exists a marginally outgoing null geodesic or each singularity is preceded by the occurrence of a closed trapped surface. The marginally outgoing null geodesics may not be admitted by general naked singularities. However, it is shown that they occur if on the Cauchy horizon the global hyperbolicity is violated in such a way that causal simplicity also does not hold. This means that a wide class of nakedly singular spacetimes is considered. This result gives some support to the validity of Penrose's hypothesis.
122 citations
TL;DR: In this paper, a number of new exact static and non-static solutions of (2+1) general relativity with scalar field, perfect fluid and magnetic field sources are presented and studied in detail.
Abstract: We extend what is known about the structure of (2+ 1)-dimensional gravitational field theories. The non-existence of any Newtonian limit to these theories is investigated in the presence of Brans-Dicke scalar fields and non-linear curvature terms in the gravita- tional action. A number of new exact static and non-static solutions of (2+1) general relativity with scalar field, perfect fluid and magnetic field sources are presented and studied in detail. Some of these possess a correspondence with (3 + 1) solutions of general relativity through a Kaluza-Klein type reduction and exhibit the 'wedge' structure of (3 + 1)- dimensional solutions describing line sources like vacuum strings. An algebraic classification of (2+ 1) gravitational fields is derived using the Bach-Weyl tensor. The description of the general cosmological solution is given in terms of arbitrary spatial functions independently specified on a spacelike surface of constant time together with a series approximation to spacetime in the vicinity of a general cosmological singularity. Various results and conjectures regarding spacetime singularities are given. Two exact cosmological solutions containing self-interacting scalar fields that produce inflationary behaviour are also found.
122 citations
TL;DR: In this article, supersymmetric Chern-Simons terms for N>or=2 extended supergravity in d=3 dimensions were presented and they were shown to be the gauge actions of N> or=2 conformal supergravity.
Abstract: The authors present supersymmetric Chern-Simons terms for N>or=2 extended supergravity in d=3 dimensions and show that they are the gauge actions of N>or=2 conformal supergravity. In these models, gravitational and gauge Chern-Simons terms (which, when coupled to other systems, give rise to self-dual vectors and/or topological mass terms) are unified by supersymmetry.
119 citations
TL;DR: The zero tension limit of the classical bosonic string is discussed in this paper, where the world sheet is a null surface and each point of the string moves independently along a null geodesic.
Abstract: The zero tension limit of the classical bosonic string is discussed. The world sheet is a null surface and each point of the string moves independently along a null geodesic.
107 citations
TL;DR: In this paper, it was shown that in addition to the d=5, N=2 MESGT theories associated with Jordan algebras, there is one other class with a symmetric target space which yields the non-compact CPn models of Luciani (1978), upon dimensional reduction to four dimensions.
Abstract: The authors show that in addition to the d=5, N=2 Maxwell-Einstein supergravity theories (MESGT) associated with Jordan algebras there is one other class with a symmetric target space which yields the non-compact CPn models of Luciani (1978), upon dimensional reduction to four dimensions. It follows that all d=4 symmetric space MESGT have their origin in d=5. They also begin an investigation into 'kinky supergravities', i.e. those for which the target manifold interpolates between two symmetric spaces. They point out that d=5, N=2 MESGT are related to d=11 supergravity by compactification on Calabi-Yau spaces.
98 citations
TL;DR: In this paper, the authors find all spatially homogeneous solutions of the Einstein field equations which have an orthogonal perfect fluid as source, or are vacuum, and admit a similarity group H4 which acts transitively on spacetime.
Abstract: It is known that the symptotic states of a large class of spatially homogeneous cosmological models, near the big bang and at late times, are described by exact self-similar solutions. With this as motivation the authors find all spatially homogeneous solutions of the Einstein field equations which have an orthogonal perfect fluid as source, or are vacuum, and admit a similarity group H4 which acts transitively on spacetime.
97 citations
TL;DR: In this article, the most general gravity Lagrangian in more than four dimensions is considered which leads to field equations with at most second derivatives of the metric, which allows spontaneous compactification.
Abstract: The most general gravity Lagrangian in more than four dimensions is considered which leads to field equations with at most second derivatives of the metric. It consists of a series of dimensionally continued Euler forms and allows spontaneous compactification. The field equations are elaborated for the usual Kaluza-Klein cosmology ansatz and solved in the special case where the extra dimensions form a sphere with constant radius. The dimensional reduction of the theory to four dimensions is discussed as well.
94 citations
TL;DR: In this article, a new way of introducing auxiliary fields into the ten-dimensional supersymmetric Yang-Mills theory was proposed, and the auxiliary fields are called pure spinors and constitute a non-linear realisation of the Lorentz group.
Abstract: The author proposes a new way of introducing auxiliary fields into the ten-dimensional supersymmetric Yang-Mills theory. The auxiliary fields are commuting 'pure spinors' and constitute a non-linear realisation of the Lorentz group. This invalidates previous no-go theorems concerning the possibility of going off-shell in this theory. There seems to be a close relation between pure spinors and the concepts usually used in twistor theory. The non-Abelian theory can be constructed for all groups having pseudo-real representations.
90 citations
TL;DR: In this paper, the unconstrained superfield formulation of D = 2, N = 1 supergravity and general matter couplings were constructed and a new type of non-linear sigma model that possesses (local supersymmetry) was described.
Abstract: The authors construct the unconstrained superfield formulation of D=2, N=1 supergravity and give general matter couplings. A new type of non-linear sigma model that possesses (local supersymmetry)(X)(local supersymmetry) is described.
TL;DR: In this article, the authors constructed exact solutions to Einstein's equation containing two colliding planar shells of matter which divide spacetime into four regions, three of which are flat.
Abstract: Using methods similar to those in a previous paper, (Dray and 't Hooft 1985), the authors construct exact solutions to Einstein's equation containing two colliding planar shells of matter which divide spacetime into four regions, three of which are flat. In the appendices they consider some more general cases.
TL;DR: In this article, explicit sets of spinor nth derivatives of the Riemann curvature spinor for a general spacetime are specified for each n so that they contain the minimal number of components enabling all derivatives of order m to be expressed algebraically in terms of these sets for n
Abstract: Explicit sets of spinor nth derivatives of the Riemann curvature spinor for a general spacetime are specified for each n so that they contain the minimal number of components enabling all derivatives of order m to be expressed algebraically in terms of these sets for n
TL;DR: In this article, the dynamical structure of the theory of gravity using a time parameter whose level surfaces are null hypersurfaces in spacetime is investigated using a spacelike foliation of codimension two.
Abstract: Investigates the dynamical structure of Einstein's theory of gravity using a time parameter whose level surfaces are null hypersurfaces in spacetime. A spacelike foliation of codimension two is used in order to give an invariant kinematic description. Dynamics are analysed via a constrained Hamiltonian formalism. It is found that the Hamiltonian formulation includes both first and second class constraints. The first class constraints are associated with the invariance of the theory with respect to diffeomorphisms of the null hypersurfaces. The second class constraints are direct consequences of the choice of null time parameter.
TL;DR: In this article, the weakest possible boundary conditions for the positive energy theorem are discussed and examples of asymptotically flat (in some sense) metrics violating this theorem are given.
Abstract: The problem of the weakest possible boundary conditions for the positive-energy theorem is discussed. Examples of asymptotically flat (in some sense) metrics violating this theorem are given. A class of metrics which have well defined infinite ADM mass is presented.
TL;DR: In this article, it was shown that the harmonic superspace Lagrangian L(+4)=1/4((D++ omega )2-( xi ++)2 omega -2) for a single interacting hypermultiplet describes an N=2 supersymmetric hyper-Kahler sigma model with the d=4 Eguchi-Hanson instanton as its target manifold.
Abstract: Harmonic superspace provides a framework for constructing general hyper-Kahler metrics. The simple example of the Taub-NUT manifold has been given previously. Here it is shown that the harmonic superspace Lagrangian L(+4)=1/4((D++ omega )2-( xi ++)2 omega -2) for a single interacting hypermultiplet describes an N=2 supersymmetric hyper-Kahler sigma model with the d=4 Eguchi-Hanson instanton as its target manifold. The potential omega -2 is the unique one invariant with respect to a Pauli-Gursey-like SU(2) group. The authors present other harmonic superspace actions which they expect to yield some other interesting metrics, including the multi-Eguchi-Hanson and Calabi ones, etc.
TL;DR: In this paper, the authors evaluate the corrections to the usual linear relation between the scalar curvature and the trace of the energy-momentum tensor, R approximately T, replacing the usual Einstein-Hilbert Lagrangian R by an unknown function f(R) and imposing the inflationary solution upon the scale factor a(t) of the Robertson-Walker metric.
Abstract: The inflationary model proposed by Guth (1981), is based on non-classical behaviour of the energy-momentum tensor. The authors try to evaluate the corrections to the usual linear relation between the scalar curvature and the trace of the energy-momentum tensor, R approximately T, replacing the usual Einstein-Hilbert Lagrangian R by an unknown function f(R) and imposing the inflationary solution upon the scale factor a(t) of the Robertson-Walker metric. Solving for f(R) enables one to evaluate the corrections to the relation R approximately T, which may be developed in powers of R or T at will.
TL;DR: In this article, a new point of view towards the problem of the relationship between gravitational and quantum phenomena is proposed which is inspired by the fact that the distinction between quantum fluctuations and real statistical fluctuations in the state of a system seems not to be maintained in a variety of phenomena in which quantum and gravitational effects are both important.
Abstract: A new point of view towards the problem of the relationship between gravitational and quantum phenomena is proposed which is inspired by the fact that the distinction between quantum fluctuations and real statistical fluctuations in the state of a system seems not to be maintained in a variety of phenomena in which quantum and gravitational effects are both important. One solution to this dilemma is that quantum fluctuations are in fact real statistical fluctuations, due to some unknown, but universal, phenomena. At the same time quantum fluctuations have certain special properties which distinguish them from other types of fluctuation phenomena. The two most important of these are that the action of quantum fluctuations is non-dissipative for the special case of systems undergoing inertial motion in the absence of gravitational fields, and that the dispersion constant for quantum fluctuations for a particle is inversely proportional to the inertial mass of the particle. These properties are summarised in a set of principles which, it is proposed, govern the relationship between quantum phenomena, gravitation and inertia.
TL;DR: In this article, the detection of radiation by linearly accelerated particle detectors is discussed from the point of view of an inertial observer, and an alternative interpretation to that of Unruh (1976) is presented.
Abstract: The detection of radiation by linearly accelerated particle detectors is discussed from the point of view of an inertial observer. An alternative interpretation to that of Unruh (1976), is presented. It is argued that the main physical effect is the emission of negative energy (as compared with Minkowski space) by the detector. This is shown to be the only important effect for 'macroscopic' detectors.
TL;DR: In this paper, the authors investigated the Einstein equation for a class of (4n+4)-dimensional SU(2)-invariant metrics on S4 and R4 fiber bundles over quaternionic Kahler base manifolds.
Abstract: The authors investigate the Einstein equation for a class of (4n+4)-dimensional SU(2)-invariant metrics on S4 and R4 fibre bundles over quaternionic Kahler base manifolds. Using numerical techniques, they establish the existence of complete compact inhomogeneous Einstein spaces of this form with positive Ricci curvature, and complete non-compact inhomogeneous Einstein spaces with zero or negative Ricci curvature.
TL;DR: There is a unique Lagrangian quadratic in the curvature tensor which yields second-order field equations in dimensions greater than four as discussed by the authors, which is applied to a Kaluza-Klein theory.
Abstract: There is a unique Lagrangian quadratic in the curvature tensor which yields second-order field equations in dimensions greater than four. This Lagrangian is applied to a Kaluza-Klein theory and its cosmological implications are investigated.
TL;DR: In this article, it was shown that no self-interacting field theory for massless spin-3 fields exists, except in trivial ways, and that the three-point coupling can be constructed, but the fourpoint coupling cannot.
Abstract: The authors show that no self-interacting field theory for massless spin-3 fields exists (except in trivial ways). The three-point coupling can be constructed, but the four-point coupling cannot. They also describe an attempt to write down a gauge algebra which includes all massless spins, and comment on the relation to string theories.
TL;DR: In this paper, the Noether method is used to construct a supergravity in d = 9 coupled to n vector multiplets, each containing a real scalar, and it is shown that the scalars parametrise the coset space Hn = SO(n, 1)/SO(n).
Abstract: N=1 supergravity in d=9 coupled to n vector multiplets, each containing a real scalar, is constructed by the Noether method. It is shown that the scalars parametrise the coset space Hn=SO(n,1)/SO(n).
TL;DR: In this paper, a 4-manifold with self-dual Weyl curvature is shown to correspond to holomorphic bundles on an associated analytic space, which generalises a flat space correspondence discovered by Isenberg et al. and Witten.
Abstract: Solutions of the (full) Yang-Mills equations on a 4-manifold with self-dual Weyl curvature are shown to correspond to holomorphic bundles on an associated analytic space. This generalises a flat space correspondence discovered by Isenberg et al. (1978) and Witten (1978).
TL;DR: In this paper, the authors use previously derived results to write an action which describes the coupling of a set of string coordinates to simple unidexterous world-sheet supergravity.
Abstract: The authors use previously derived results to write an action which describes the coupling of a set of string coordinates to simple unidexterous world-sheet supergravity. They demonstrate the presence of the fermionic symmetry that implies decoupling of unphysical string states, even when local (1,0) supersymmetry is realised on the world sheet of the string.
TL;DR: In this paper, the authors define the data of a 2-surface S in spacetime in terms of its first and second fundamental forms and show how Penrose's kinematic twistor for S is a functional of these data.
Abstract: The author defines the 'data' of a 2-surface S in spacetime in terms of its first and second fundamental forms and show how Penrose's kinematic twistor for S is a functional of these data. The author finds necessary and sufficient conditions in terms of the data for S to be 'contorted', i.e. for its data not to be the data of a 2-surface in a conformally flat space, and show that S is non-contorted iff the usual (local) twistor definition of norm is in fact constant on S. They find a large class of non-contorted 2-surfaces in the Schwarzchild solution and show that the Penrose mass MP to whether one of this class is zero or Ms, the Schwarzchild mass parameter, according to whether the 2-surface does not or does go round the central hole. Finally, they calculate the 2-surface twistor space for a stationary black hole and prove the 'isoperimetric inequality' for the Penrose mass of a static black hole.
TL;DR: In this paper, the stability condition of the four-dimensional Friedmann universe with a compact internal space (F4*KD) was analyzed for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space.
Abstract: The stability condition of (the four-dimensional Friedmann universe)*(a compact internal space) (F4*KD) is presented for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space. The Candelas-Weinberg model (i.e. one-loop quantum correction+a cosmological constant Lambda ), eleven-dimensional supergravity+ Lambda , Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F4*KD solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. The author finds that the stable F4*KD solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.
TL;DR: In this paper, a technique for extending general relativity called algebraic extension was shown to yield only five classes of gravitational theories (general relativity plus four extensions), and it was shown that only one of these extensions is ghost free.
Abstract: Recently a technique for extending general relativity called algebraic extension was shown to yield only five classes of gravitational theories (general relativity plus four extensions). The particle spectra of these theories are analysed and it is shown that only one of these extensions is ghost free. Two inequivalent theories are shown to result from this extension at the linearised level. One of these is the linearised version of Moffat's theory of gravitation (1979) the other is a new theory which possesses an additional gauge invariance which has been associated with a closed string.
[...]
TL;DR: In this article, it was shown that the previously proposed form of supergravity with 32 off-shell components (instead of the usual 24 for minimal or 40 for non-minimal) is reducible, and represents only a particular coupling of super gravity to a scalar multiplet.
Abstract: The author shows that the previously proposed form of supergravity with 32 off-shell components (instead of the usual 24 for minimal or 40 for non-minimal) is reducible, and represents only a particular coupling of supergravity to a scalar multiplet.
TL;DR: In this paper, a formalism for quantum Regge calculus in the Lorentzian domain, calculating the inverse propagator in the free field case, is presented. But the authors do not specify the corresponding variables in the Arnowitt-Deser-Misner 3+1 formulation of general relativity.
Abstract: The author sets up a formalism for quantum Regge calculus in the Lorentzian domain, calculating the inverse propagator in the free field case. The author relates the variables in the Arnowitt-Deser-Misner 3+1 formulation of general relativity to the Regge calculus variables.