Table of contents

The full metric representing a charged generalization of the Gutsunaev-Manko stationary vacuum solution is given in the explicit form.

It is shown that the problem of nonobservation of quadrupole anisotropy of cosmic background radiation can be solved by means of choosing some relevant initial conditions on the quantized scalar field in the framework of inflation. Moreover, the extremely small value of the inflaton potential constant may also be increased in this way.

Some noncompact sigma -models arise in the process of the dimensional reduction of (super)gravity-matter systems. These sigma -models have to be invariant under Abelian shifts of those scalar fields that are produced by duality transformations. The authors observe that such isometries form light-like Abelian subgroups of the full sigma -model isometry groups. This fact will facilitate the study of the correspondence between some quaternionic and special Kahler manifolds (c*-map) arising in superconformal field theories.

Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a nonperturbative treatment of the quantum theory. The aim of this paper is to provide a mathematical basis for this proposal. The quantum holonomy algebra is constructed, and, in the case of real connections, given the structure of a certain C*-algebra. A proper representation theory is then provided using the Gel'fand spectral theory. A corollary of these general results is a precise formulation of the 'loop transform' proposed by Rovelli and Smolin (1990). Several explicit representations of the holonomy algebra are constructed. The general theory developed here implies that the domain space of quantum states can always be taken to be the space of maximal ideals of the C*-algebra. The structure of this space is investigated and it is shown how observables labelled by 'strips' arise naturally.

Two particular aspects of the quantization of systems with first class linear momentum constraints are discussed. First, the inequivalence between Dirac and reduced phase space quantization is explained in terms of an ambiguity in the ordering of gauge invariant operators in the reduced Hamiltonian. It is shown that this operator ordering ambiguity arises due to a potential contribution to the reduced Hilbert space measure from the volume of the gauge orbit over each point in the physical configuration space. Secondly, the relationship between the gauge fixed covariant Faddeev-Popov functional integral and the functional integral for the completely reduced theory is elucidated. In particular, it is shown explicitly how the Faddeev-Popov functional integral reduces to the functional integral obtained via reduced phase space quantization, despite the fact that the measure of the former contains a contribution from the volume of the covariant gauge orbits, while the latter retains no information about the gauge structure.

The authors examine 't Hooft's prescription (1985) for cutting off eigenmodes of particle wavefunctions in the vicinity of black hole event horizons in N dimensions. They find for any N>3 that the cutoff occurs as a consequence of the causal structure of spacetime independently of the strength of the source, in agreement with the four-dimensional case. They separately discuss the special case N=2, showing why in this case the cutoff depends on the strength of the source.

The author considers a conformally invariant Lagrangian for a scalar field psi on a two-dimensional surface with Weyl geometry defined by a metric g_{mu nu} and a gauge vector phi ^mu . The effective action for the gravitational field induced by 'integrating out' psi is shown to be itself conformally invariant provided phi ^mu is subject to a finite renormalization. Applying the equation of motion for phi ^mu results in a purely topological action.

This paper studies the 1-loop effective potential and spontaneous-symmetry-breaking pattern for SU(5) gauge theory in de Sitter spacetime. Curvature effects modify the flat-space effective potential by means of a very complicated special function previously derived in the literature. An algebraic technique already developed by Buccella et al. to study spontaneous symmetry breaking of SU(n) for renormalizable polynomial potentials is here generalized, for SU(5), to the much more difficult case of a de Sitter background. A detailed algebraic and numerical analysis provides a better derivation of the stability of the extrema in the maximal subgroups SU(4)*U(1), SU(3)*SU(2)*U(1), SU(3)*U(1)*U(1)*R₃₁₁, SU(2)*SU(2)*U(1)*U(1)+R₂₂₁₁, where R₃₁₁ and R₂₂₁₁ discrete symmetries select particular directions in the corresponding two-dimensional strata. One thus obtains a deeper understanding of the result, previously found with a different numerical analysis, predicting the slide of the inflationary Universe into either the SU(3)*SU(2)*U(1) or SU(4)*U(1) extremum. Interestingly, using this approach, one can easily generalize all previous results to a more complete SU(5) tree-level potential also containing cubic terms.

The authors reduce the cosmological model of extended inflation to a spatially flat Robertson-Walker geometry driven by a self-interacting scalar field with a potential of an exponential type. They quantize the gauge invariant scalar perturbations of the metric and the field, and compute the spectrum of the energy density fluctuations.

A technique for constructing first integrals is used to regain two orthogonal Bianchi perfect fluid solutions in a unified way and to find an apparently new Bianchi type-V tilted solution with stiff fluid. The solution includes a big bang model which is asymptotically tilted.

The authors point out that the classical Einstein field equations, suitably interpreted, allow a change of signature of spacetime. Specific examples of such changes are constructed in the case of Robertson-Walker geometries. They obtain classical solutions that have properties similar to those obtained in quantum cosmologies obeying the Hartle-Hawking 'no boundary' condition: these singularity-free universes have no beginning, but they do have an origin of time. They can be regarded either as classical analogues of the quantum cosmology results, or as classical solutions where a quantum cosmology era is avoided.

In a first-order Lagrangian theory of gravitation, the author proves rigorously that general coordinate transformations are Noetherian symmetries if and only if the Lagrangian is a linear combination of a cosmological term and of a Lagrangian giving Einstein equations. Only the pure gravity case is considered.

It is shown that in many cases nontrivial Killing tensors and conformal Killing tensors can be obtained explicitly without having to solve the usually cumbersome Killing tensor equations just by knowing the Killing vectors and conformal Killing vectors of a spacetime. Two examples are given, the first is one of the Kimura metrics and the second an unphysical spacetime constructed to illustrate the method.

The hoop conjecture of Thorne (1972) is studied for trapped surfaces produced by a construction of Gibbons and Penrose (1973). Some formulations of the conjecture are proved and others are shown to be false. It is also shown how cylindrical trapped surfaces may form in cylindrical collapse.

The authors examine the gravitational coupling of Klein-Gordon and Dirac fields to matter vorticity and spacetime torsion, in the context of Einstein-Cartan theory. The background spacetime is endowed with a Godel-type metric, characterized by two real parameters ( Omega , l²); the source of spacetime curvature is a Weyssenhoff-Raabe fluid with spin vector parallel to the vorticity field. They show that torsion and matter vorticity have identical effects on the physics of particle fields. Complete sets of solutions are obtained, satisfying boundary conditions connected to the test-field character of the solutions. The energy spectrum obtained is discrete in general, except for the case of hyperbolic Godel-type geometries (l²>0) where a continuum region in the energy spectrum may appear: if 0< Omega ²<l² a continuum region is present in the upper part of the spectrum; if Omega ²>or=l², Dirac solutions may present, under certain conditions, a continuum region in the lower part of the spectrum. The correspondence between classical geodesic motion and Klein-Gordon solutions is established, and used as a guide to select the correct boundary conditions for the test fields. Matter vorticity and/or spacetime torsion split the energy spectrum of Dirac particles. These effects are additive and result from the existence of the same constant of motion for both cases. This constant of motion generates a trivial symmetry of the system in Minkowski spacetime, the associated degeneracy of which is raised by matter vorticity and/or torsion fields, producing the above-mentioned split.

The author shows that quantum fluctuations, in particular vacuum polarization, vanish in the background of the spherical shock wave solution of the Einstein field equations, recently found by Nutku (1991). This result is due to the smoothness properties of the new solution.

In the calculations of the contributions of massless fields to 1-loop effective potentials on spacetimes of the form R^m*T^d, it is known that infrared divergences can only be avoided if the Euclidean space dimension m is greater than 2. In recent papers dealing with vanishing gauge background, such infrared divergences are confined to the toroidal zero momentum mode, and it has been claimed that this mode should therefore be ignored in the subsequent analysis. However, as there can exist nontrivial 'flat' gauge vacua on nonsimply connected manifolds, then such backgrounds must be included in any analysis on the torus. As a consequence, it is shown that, even if the infrared divergent zero momentum mode is discarded, the remaining contributions to the 1-loop potential still exhibit poor infrared behaviour at certain nonzero gauge background configurations. As a result, any conclusions drawn previously on the assumption of finiteness of the nonzero mode contributions must be considered invalid.

It is shown that Christodoulou's recently discovered memory effect (1991) can easily be derived from the well known Newman-Unti asymptotic solution of the vacuum Einstein equations.

The validity of the JWKB approximation as applied to black hole normal modes is discussed as a possible source of the discrepancy between the quasinormal frequency values computed by Guinn et al. in their recent letter (1990) and those computed by the method of continued fractions. For Regge-Wheeler-like potentials and large frequency magnitudes, an analytic JWKB approximation is suggested that can be expressed in terms of complete elliptic integrals.