Showing papers in "Classical and Quantum Gravity in 1984"
TL;DR: In this article, a new approach to N = 2 supersymmetry based on the concept of harmonic superspace is proposed and is used to give an unconstrained superfield geometric description of N=2 super Yang-Mills and supergravity theories as well as of matter N =2 hypermultiplets.
Abstract: A new approach to N=2 supersymmetry based on the concept of harmonic superspace is proposed and is used to give an unconstrained superfield geometric description of N=2 super Yang-Mills and supergravity theories as well as of matter N=2 hypermultiplets. The harmonic N=2 superspace has an independent coordinates, in addition to the usual ones, the isospinor harmonics ui+or- on the sphere SU(2)/U(1). The role of ui+or- is to relate the SU(2) group realised on the component fields to a U(1) group acting on the relevant superfields. Their introduction makes it possible to SU(2)-covariantise the notion of Grassmann analyticity. Crucial for the construction is the existence of an analytic subspace of the general harmonic N=2 superspace. The hypermultiplet superfields and the true prepotentials (pre-prepotentials) of N=2 super Yang-Mills and supergravity are unconstrained superfunctions over this analytic subspace. The pre-prepotentials have a clear geometric interpretation as gauge connections with respect to the internal SU(2)/U(1) directions. A radically new feature arises: the number of gauge and auxiliary degrees of freedom becomes infinite while the number of physical degrees of freedom remains finite. Other new results are the massive N=2 Yang-Mills theory and various off-shell self-interactions of hypermultiplets. The propagators for matter and Yang-Mills superfields are given.
907 citations
TL;DR: In this paper, the structure of the gravitational field at infinity of asymptotically anti-de Sitter space-time is analyzed in detail using conformal techniques, and definitions of 'conserved' quantities at J in terms of the curvature tensor which are free of the ambiguities present in the previous definitions are introduced.
Abstract: The structure of the gravitational field at infinity of asymptotically anti-de Sitter space-time is analysed in detail using conformal techniques. It is found that the situation differs from that in the case of asymptotically Minkowskian space-times in a number of respects, primarily because J is now time-like rather than null. In particular, the asymptotic symmetry group is quite different from the BMS group, and there is no analogue of the Bondi news. The analysis also introduces definitions of 'conserved' quantities at J in terms of the curvature tensor which are free of the ambiguities present in the previous definitions based on the deviation of the physical metric from an anti-de Sitter background.
417 citations
TL;DR: In this paper, the authors show that all known solutions of the N=2 non-chiral d=10 supergravity theory can, by a simple procedure, be obtained from the known Freund-Rubin type solutions of D=11 supergravity.
Abstract: The authors show that all known solutions of the N=2 non-chiral d=10 supergravity theory can, by a simple procedure, be obtained from the known Freund-Rubin type solutions of D=11 supergravity. This is a consequence of the fact that each solution of the d=10 theory depends crucially on the presence of a topologically non-trivial U(1) field strength Fmn. The mass spectrum of a particular d=10 solution is obtained by truncating the spectrum of the corresponding d=11 solution to the subset of fields neutral under the non-trivial U(1) symmetry. They investigate the compactification on CP3, and show that this yields a theory with N=6 or N=0 supersymmetry according to the orientation, and they relate this to the S7 compactification of d=11 supergravity. Starting from the squashed S7 in d=11 they derive a new solution of the d=10 theory, namely (AdS)4 times CP3 with a squashed non-Einstein metric. The supersymmetry is either N=1 or N=0 depending on the orientation. They conjecture that none of the supergravity theories in 4
267 citations
TL;DR: In this article, a revised model of the inflationary universe under the framework of Brans-Dicke theory is proposed, and it is shown that the scale factor of the universe during the inflation varies as R approximately tw+1/2 and not exponentially, but still it gives rise to enough inflation to solve the cosmological puzzles.
Abstract: A revised model of the inflationary universe under the framework of Brans-Dicke theory is proposed. It is shown that the scale factor of the universe during the inflation varies as R approximately tw+1/2 and not exponentially, but still it gives rise to enough inflation to solve the cosmological puzzles. It is found that the quantum gravity effects come into play in the same scale as that of grand unified theories (i.e. at T approximately 1014 GeV) rather than at T approximately 1019 GeV, hence providing a natural solution to the 'milder version' of the flatness problem inherent in the conventional inflationary scenarios. This scenario also provides a simple way to estimate theoretically the present value of the gravitational constant. The estimated value agrees well with the actual value despite many approximations and the ignorance of quantum gravity; the difference is only by a factor of the order of 10-2.
192 citations
TL;DR: In this article, the origin dependence of Penrose's angular momentum is shown to have the correct form, and the authors then define a momentum for all elements of the BMS Lie algebra, which is the first such expression with the property that its flux vanishes identically in Minkowski space.
Abstract: The definition of angular momentum recently given by Penrose (1982) is analysed on I. It is shown that this definition is essentially a supertranslation of previous definitions. The origin dependence of Penrose's angular momentum is shown to have the correct form. Based on Penrose's expression, the authors then define a momentum for all elements of the BMS Lie algebra, which is the first such expression with the property that its flux vanishes identically in Minkowski space.
136 citations
TL;DR: In this article, it is suggested that there is also an uncountably infinite but still discrete set of perpetually bouncing aperiodic solutions, which appear to form a fractal with positive Hausdorff-Besicovitch dimension.
Abstract: For a Friedman-Robertson-Walker universe minimally coupled to a massive scalar field, Hawking (1983) has shown that there is a countably infinite discrete set of periodic solutions which bounce without a singularity. Here it is suggested that there is also an uncountably infinite but still discrete set of perpetually bouncing aperiodic solutions. The latter set appears to form a fractal with positive Hausdorff-Besicovitch dimension.
113 citations
TL;DR: In this article, a comprehensive study of spatially homogeneous and SO(3)-isotropic exact solutions of the 10-parameter Lagrangian of the 'Poincare gauge theory' is presented.
Abstract: This is a comprehensive study of spatially homogeneous and SO(3)-isotropic exact solutions of the 10-parameter Lagrangian of the 'Poincare gauge theory'. Some sets of new exact solutions are presented. In particular, all solutions following from the so-called modified double quality ansatz are obtained, up to integration of some familiar ordinary differential equations. For certain classes of solutions, the occurrence of torsion singularities is discussed in detail. Furthermore, the authors investigate whether some solutions without metric singularity can provide reasonable cosmological models.
92 citations
TL;DR: In this paper, a simple and natural realisation of the chaotic inflation scenario in the context of SU(1,1) supergravity is suggested in order to explain the randomness of inflation.
Abstract: A simple and natural realisation of the chaotic inflation scenario is suggested in the context of SU(1,1) supergravity.
76 citations
TL;DR: The formalism of spherical harmonics for coset spaces is used to obtain the complete mass spectrum of the bosonic excitations around a class of vacuum solutions of d = 11 supergravity in which the internal space is a coset manifold and the three-index photon is given by the Freund-Rubin ansatz as discussed by the authors.
Abstract: The formalism of spherical harmonics for coset spaces is used to obtain the complete mass spectrum of the bosonic excitations around a class of vacuum solutions of d=11 supergravity in which the internal space is a coset manifold and the three-index photon is given by the Freund-Rubin ansatz (1978). The mass formula is given in terms of the eigenvalues of the invariant operators on the internal space.
71 citations
TL;DR: In this paper, an approach to quantisation in terms of a transitive group of symplectic transformations of the classical phase space is discussed, and it is shown that the appropriate canonical algebra (i.e. the analogue of the canonical commutation relations for the case of a linear phase space) is that of the affine commutation relation.
Abstract: An approach to quantisation in terms of a transitive group of symplectic transformations of the classical phase space is discussed. This is applied to general relativity where the phase space is nonlinear and it is shown that the appropriate canonical algebra (i.e. the analogue of the canonical commutation relations for the case of a linear phase space) is that of the affine commutation relations.
67 citations
TL;DR: In this article, the coupled massless spin-5/2-Einstein system exhibits a new local supersymmetry parametrised by a vector-spinor rather than a spinor as in supergravity.
Abstract: In three spacetime dimensions, the coupled massless spin-5/2-Einstein system exhibits a new local supersymmetry parametrised by a vector-spinor rather than a spinor as in supergravity. Although the theory does not contain dynamics, but only torsion, this hypersymmetry still formally ensures consistency. The analysis extends to arbitrary rank fermions.
TL;DR: In this paper, the free energy of a scalar field in the product manifold R*Rn*Md. is studied and the role and effect of zero modes is considered.
Abstract: Some general formulae, including high and low temperature forms, are developed for the free-energy of a scalar field in the product manifold R*Rn*Md. The role and effect of zero modes is considered and specific calculations are made for the cases when the internal space, Md, is a torus and a sphere.
TL;DR: For covariantly chiral superfields coupled to background Yang-Mills superfields and defined on a curved superspace background, the superfield analogue of the heat kernel associated with the differential operator appearing in the quadratic part of the action is defined in this paper.
Abstract: For covariantly chiral superfields coupled to background Yang-Mills superfields and defined on a curved superspace background, the superfield analogue of the heat kernel associated with the differential operator appearing in the quadratic part of the action is defined. The super-b4 coefficient in the asymptotic expansion of the kernel is computed using a system of superspace normal coordinates. These coefficients are shown to determine the one-loop trace supermultiplet and the one-loop logarithmic divergence for pure supergravity.
TL;DR: In this paper, a unified representation of the canonical group C for quantum gravity is studied, producing concrete operator realisations of the basic canonical fields eAB, pi CD of the theory together with its spatial diffeomorphism group covariance.
Abstract: For pt.I see ibid., vol.1, p.621-32, 1984. Unitary representations of the canonical group C for quantum gravity, discussed in an earlier paper, are studied producing concrete operator realisations of the basic canonical fields eAB, pi CD of the theory together with its spatial diffeomorphism group covariance. The appropriate state functionals are concentrated on distributional triads and not smooth ones. In addition, for a class of these representations the distributional triads are also degenerate, a feature does not appear for the conventional canonical commutation relations and the weak-field perturbation framework.
TL;DR: By using the geometric structure of the Wess-Zumino formulation of N = 1 supergravity, a normal coordinate system is defined locally in curved superspace, and the normal coordinate expansions for the supervielbein and connection coefficients are derived as mentioned in this paper.
Abstract: By using the geometric structure of the Wess-Zumino formulation of N=1 supergravity, a normal coordinate system is defined locally in curved superspace, and the normal coordinate expansions for the supervielbein and connection coefficients are derived.
TL;DR: In this article, a new exact solution of the field equations with the energy-momentum tensor of a perfect fluid is given, which can be interpreted as a stationary axisymmetric gravitational field which is regular and satisfies the dominant energy condition everywhere inside a closed surface of vanishing pressure.
Abstract: A new exact solution of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. This solution can be interpreted as a stationary axisymmetric gravitational field which is regular and satisfies the dominant energy condition everywhere inside a closed surface of vanishing pressure. The fluid rotates rigidly; the equation of state is epsilon +3p=constant. The solution is of Petrov type D and admits a maximal group G2 of motions.
TL;DR: In this article, the spectrum of representations contributing to the zero, one, two, three and four-forms on Mpqr spaces was determined and the eigenvalues of the Laplacian on zero-forms and of the *d operator on three-forms were calculated.
Abstract: The authors determine the spectrum of the representations contributing to the zero, one, two, three-forms on Mpqr spaces: then, they calculate the eigenvalues of the Laplacian on zero-forms and of the *d operator on three-forms. These latter can be given only implicitly since they are the roots of a 15th-order secular equation. In the sector of the two-forms there is a zero-mode corresponding to the fact that the second Betti number B2 is equal to one. Hence there is an extra U1 vector multiplet and the effective theory in four-dimensions is N=2 supergravity coupled to the N=2 gauge multiplet of SU(3)(X)SU(2)(X)U(1). There are also scalar zero-modes in the (10,3) and (10,3) of SU(3)(X)SU(2). They show that they are not elements of a N=2 hypermultiplet but rather of a bigger multiplet containing also vectors and other spins. Hypermultiplets whose states are all massive are not excluded and using the results of the spectrum can now be systematically searched.
TL;DR: In this article, the structural theorem of decomposition of a free differential algebra into a contractible and minimal one is utilised to given an intrinsic definition of the concepts of curvatures and potentials in gauge theories including antisymmetric tensors.
Abstract: The structural theorem of Sullivan of the decomposition of a free differential algebra into a contractible and minimal one is utilised to given an intrinsic definition of the concepts of curvatures and potentials (=connections) in gauge theories including antisymmetric tensors. Applying this idea to d=11 supergravity the author clarifies the role of the 6-index photon showing that all d=11 field equations are a consequence of the principle of rheonomy inserted into the complete differential algebra encompassing both the 3- and 6-forms. Moreover the 6-index photon is dual to the 3-index one as a consequence of the algebra. This is close analogy with the relation between the axion and the dilaton in conformal supergravity. Finally the action of the d=11 theory has a simpler formulation in terms of the curvatures of the full differential algebra.
TL;DR: In this article, the authors give explicit expressions for the charge integral associated with an arbitrary BMS vector at a given retarded time by weakening the definition of angular momentum given by Penrose (1982) into a map dual to the entire BMS group.
Abstract: The symplectic approach to obtaining fluxes of gravitational energy-momentum and angular momentum given by Ashtekar and Streubel (1981) is completed by giving explicit expressions for the charge integral associated with an arbitrary BMS vector at a given retarded time. The expressions are obtained by weakening the definition of angular momentum given by Penrose (1982) into a map dual to the entire BMS group.
TL;DR: There are no static asymptotically vanishing excitations of coupled Einstein-Yang-Mills theory in three-dimensional spacetime as mentioned in this paper, and no static vanishing excitation of coupled EYM theory in 3-dimensional space.
Abstract: There are no static asymptotically vanishing excitations of coupled Einstein-Yang-Mills theory in three-dimensional spacetime.
TL;DR: In this article, a formalism for the mathematical description of conformal gravity and its dynamical evolution based on the local twistor geometry is presented, and it is shown that the electromagnetic field can naturally be incorporated into this scheme by a modification of the LSTM.
Abstract: A formalism for the mathematical description of conformal gravity and its dynamical evolution based on the local twistor geometry is presented. It is shown that the electromagnetic field can be naturally incorporated into this scheme by a modification of the local twistor parallel transport law. The dynamical equations (the Bach equations for gravity and the Maxwell equations for the electromagnetic field) are obtained by varying a single quantity-the modified twistor connection.
TL;DR: In this paper, a mathematically consistent global theory of super fibre bundles is laid down and a rigorous analysis of the construction of super fiber bundles, connections, reduced bundles and reduced connections is performed.
Abstract: A mathematically consistent global theory of super fibre bundles is laid down. In this framework the authors perform, in a rigorous way, the analysis of the construction of super fibre bundles, connections, reduced bundles and reduced connections. Some bundles of physical interest, constructed over a supermanifold (the Lorentz bundle and the graded Poincare bundle), are analysed in detail. A criterion for the existence of a Lorentz bundle over a supermanifold is established. Some results about subgroups of super Lie groups are also given.
TL;DR: In this paper, the back reaction equations for a spherically symmetric evaporating black hole space-time were investigated and a solution which reproduces Hawking's formula for the evaporation rate was shown to exist.
Abstract: The back reaction equations for a spherically symmetric evaporating black hole space-time are investigated. A solution which reproduces Hawking's formula for the evaporation rate is shown to exist.
TL;DR: In this paper, the SL(2) formalism of Kinnersley and Chitre (1978) for generating techniques in stationary axisymmetric vacuum space-times is adapted to work for space times with two spacelike commuting Killing vectors.
Abstract: The SL(2) formalism of Kinnersley and Chitre (1978) for generating techniques in stationary axisymmetric vacuum space-times is adapted to work for space-times with two spacelike commuting Killing vectors. The Kinnersley-Chitre formalism is known to be explicitly related to the inverse scattering transformation of Belinskii and Zakharov (1979) which has already been applied in both types of above mentioned space-times. Using the hyperbolic versions of various Kinnersley-Chitre transformations the interrelation between various vacuum cosmological solutions is obtained. For each solution the Kinnersley-Chitre generating function FAB(t) and corresponding Belinskii-Zakharov eigenfunction psi ( lambda ) is given. These vacuum solutions are then converted to scalar field/stiff perfect fluid solutions using the algorithm of Wainwright, Ince and Marshman (1979).
TL;DR: In this article, a method for extending general relativity, called the method of algebraic extension, is presented, and it is shown under certain restrictions that only five theories of gravity, one of which is general relativistic, result from such an extension.
Abstract: A new method for extending general relativity, called the method of algebraic extension, is presented. It is shown under certain restrictions that only five theories of gravity, one of which is general relativity, result from such an extension. Lagrangians for the five theories are constructed. The relationship between algebraically extended theories and higher-dimensional theories of Riemannian gravity is outlined.
TL;DR: In this paper, the concept of particle detector equivalence was introduced and applied to three different detectors of the neutral scalar quantum field, and it was found that these detectors, in general, are not equivalent in that they will perceive a different particle content when placed in identical situations.
Abstract: A concept of 'particle detector' is presented and found to include a variety of different possible models. A method of comparing these different models is introduced and a concept of 'particle detector equivalence' is defined. This concept is then applied to three different detectors of the neutral scalar quantum field. It is found that these detectors, in general, are not equivalent in that they will perceive a different particle content when placed in identical situations. These results are consistent with the Copenhagen interpretation of quantum mechanics. The equivalence concept is also used to construct several theorems which may be useful in gaining some insight into possible symmetries between fields of different spin.
TL;DR: In this article, the authors derived vacuum solutions for inhomogeneous generalisation of Bianchi models III, V and VIh, which generalise particular exact solutions previously obtained by Carmeli and Charach (1981).
Abstract: The authors derive vacuum solutions for inhomogeneous generalisation of Bianchi models III, V and VIh. These solutions generalise particular exact solutions previously obtained by Carmeli and Charach (1981). As particular cases, they derive general vacuum solutions for homothetic models of types fIII, fV and fVIh. Some properties of these solutions are discussed, especially their singular or regular nature at the boundaries of the intervals of definition of the spacelike and timelike variables. In particular, doubts are cast on the interpretation of vacuum homothetic solutions as cosmological models.
TL;DR: In this article, the authors considered a quantised Maxwell field propagating in the gravitational field of a Schwarzschild black hole and derived the point-separated expectation value of the energy-momentum tensor in the Hartle-Hawking vacuum.
Abstract: The author considers a quantised Maxwell field propagating in the gravitational field of a Schwarzschild black hole. The vector Hartle-Hawking propagator is defined on the Riemannian section of the analytically continued space-time and expanded in terms of four-dimensional vector spherical harmonics. The equations for the radial functions appearing in this expansion are derived for both odd and even parity. Using the expansion of the vector Hartle-Hawking propagator the author then derives the point-separated expectation value of the Maxwellian energy-momentum tensor in the Hartle-Hawking vacuum. The renormalised values of radial pressure, tangential pressure and energy density are obtained near the horizon of the black hole. The author thus extends previous work of various authors on vacuum polarisation of a massless scalar field near a black hole to the more realistic case of the Maxwell field. In contrast to the scalar field, the Maxwell field exhibits a positive energy density near the horizon in the Hartle-Hawking vacuum state.
TL;DR: In this article, the authors give the constraints for N = 2 supergravity in terms of N = 1 supergravity and matter fields and solve the constraints to second order in the matter fields, keeping full nonlinearity in the N=1 supergravity fields.
Abstract: The authors give the constraints for N=2 supergravity in terms of N=1 supergravity and matter fields. They solve the constraints to second order in the matter fields, keeping full nonlinearity in the N=1 supergravity fields, and give the action to the same order. This is sufficient for one-loop background superfield calculations.
TL;DR: In this paper, Dirac's canonical formalism is applied to the Lagrangian of the linear approximation in the non-symmetric theory of gravitation proposed by Moffat (1979, 1982).
Abstract: Dirac's canonical formalism is applied to the Lagrangian of the linear approximation in the non-symmetric theory of gravitation proposed by Moffat (1979, 1982). Five dynamical degrees of freedom are found to exist in addition to the two graviton modes of general relativity. Although the Hamiltonian describing these five degrees of freedom is not bounded below, it is shown that there exists a unique subdynamics with positive definite Hamiltonian which contains precisely the single 'skewon' mode discussed in previous work.