Table of contents

Massless scalar fields at finite temperature are considered in four-dimensional ultrastatic curved spacetime. The one-loop non-local effective action at finite temperature is found up to second order in the curvature expansion. This action is explicitly infrared finite. In the high-temperature expansion of the free energy, essentially non-local terms linear in temperature are derived.

Recently Bernd Schmidt has given three explicit examples of spacetimes with toroidal null infinities. In this paper all solutions with a toroidal null infinity within Schmidt's metric ansatz (polarized Gowdy models) are constructed. The members of the family are determined by two smooth functions of one variable. For the unpolarized Gowdy models the same kind of analysis carries through.

The proposed space mission Galileo Galilei (GG) utilizes Earth-orbiting test masses in high-speed co-rotation to test the Weak Equivalence Principle (EP). This paper presents the results of a technical evaluation of the proposal, as it was presented in September 1996. Investigation of the dynamics and control aspects reveals that the experiment is limited by the imperfections inherent in the practical implementation of the required drag-free control and stabilizing servo forces. The net consequence is a degradation of the EP measurement sensitivity by many orders of magnitude compared with the proposers' expectations.

Spin- gauge fields are quantized in an irreducible way using both the BRST and BRST-anti-BRST methods. To this end, we transform the reducible generating set into an irreducible one, such that the physical observables corresponding to these two formulations coincide. The gauge-fixing procedure emphasizes, on the one hand, the differences between our procedure and the results obtained in the literature and, on the other hand, the equivalence between our BRST and BRST-anti-BRST approaches.

The problem of the motion of extended, i.e. non-point, test bodies in multidimensional space is discussed. Extended bodies are described in terms of so-called multipole moments. Using an approximate form of the equations of motion for extended bodies, deviation from geodesic motion is derived. The results are applied to a special form of spacetime.

We generalize the action found by 't Hooft, which describes the gravitational interaction between ingoing and outgoing particles in the neighbourhood of a black hole. The effect of this back-reaction is that of a shock wave, and it provides a mechanism for recovering information about the momentum of the incoming particles. The new action also describes particles with transverse momenta and takes into account the transverse curvature of the hole, and has the form of a string theory action. Apart from the Polyakov term found by 't Hooft, we also find an antisymmetric tensor, which is here related to the momentum of the particles. At the quantum level, the identification between position and momentum operators leads to four non-commuting coordinates. A certain relation to M(atrix) theory is proposed.

There exist simple single-charge and multi-charge BPS p-brane solutions in the D-dimensional maximal supergravities. From these, one can fill out orbits in the charge vector space by acting with the global symmetry groups. We give a classification of these orbits, and the associated cosets that parametrize them.

Families of solutions to the field equations of the covariant BRST invariant effective action of membrane theory are constructed. The equations are discussed in a double-dimensional reduction; they lead to a nonlinear equation for a one-dimensional extended object. One family of solutions of these equations are solitary waves with several properties of solitonic solutions in integrable systems, providing evidence that in this double-dimensional reduction the nonlinear equations are an integrable system. The other family of solutions found exploits the property that the nonlinear system under some assumptions is equivalent to a nonlinear Schrödinger equation.

We consider a spacetime with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2) invariant. Thus they form a finite-dimensional phase space. We perform non-perturbative path-integral quantization of the model. Contrary to previous claims, the path integral measure appeared to be non-singular near configurations admitting additional Killing vectors. In this model we are able to calculate the generating functional of Green functions of the reduced phase space variables exactly.

The effects of particle creation and vacuum polarization in an external gravitational field offer one possibility to attack certain problems of classical cosmology such as the occurrence of particle horizons.

We calculate the vacuum expectation value of the stress-energy tensor of a non-conformal scalar field in a form that is suitable for studying the back-reaction effects in cosmology. The gravitational background metric is of Robertson-Walker type. By exploiting the early-time approximation, it proves possible to represent the result as an explicit functional of the scale factor. Its properties are discussed and the conformal anomaly is correctly reproduced. The density of created particles is also calculated.

The energy density is probed for the particular class of degree-type scale factors which is relevant in Friedmann cosmology. Except for the square root expansion law, it is found to depend sensitively on the curvature coupling coefficient. The new contributions can become large compared to the previously known conformal contributions and may significantly influence the initial gravitational field.

Quantum gravity has great difficulties in the application of the notion of probability. We analyse this problem according to the algorithmic viewpoint. According to Kolmogorov, the probability notion can be connected to the algorithmic complexity of a given object. We propose an interpretation of quantum gravity, according to which the appearance of something corresponds to its Kolmogorov algorithmic complexity. From this viewpoint the following questions are considered: a quantum transition with supplementary coordinates splitting off, the estimation of the algorithmic complexity of the Schwarzschild black hole, the redefinition of the Feynman path integral and the quantum birth of the Euclidean universe with the following change of the metric signature.

We use a computer to follow the evolution of two gravitating particles in a (2 + 1)-dimensional closed universe. In a closed universe there is enough energy to produce a Gott-pair, i.e. a pair of particles with tachyonic centre of mass, from regular initial data. We study such a pair and find that they can wind around each other with ever increasing momentum. As was shown by 't Hooft, the universe must crunch before any closed timelike curve can be traversed. We study the two-particle system and quantize it, long before this crunch happens, in the high-momentum limit. We find that both the relevant configuration variable and its conjugate momentum become discretized.

A large variety of spacetimes - including the BTZ black holes - can be obtained by identifying points in (2 + 1)-dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained under a restriction to time-symmetric initial data and one asymptotic region only. The resulting spacetimes are non-eternal black holes with collapsing wormhole topologies. Our approach is geometrical, and we discuss in detail the allowed topologies, the shape of the event horizons, topological censorship and trapped curves.

The well known monopole solution of Barriola and Vilenkin (BV) resulting from the breaking of a global SO(3) symmetry is extended in general relativity along with a zero-mass scalar field and also in the Brans-Dicke (BD) theory of gravity. In the case of BD theory, the behaviour of spacetime and other variables such as the BD scalar field and the monopole energy density have been studied numerically. For a monopole along with a zero-mass scalar field, exact solutions are obtained and, depending upon the choice of arbitrary parameters, the solutions either reduce to the BV case or to a pure scalar field solution as special cases. It is interesting to note that unlike the BV case the global monopole in the BD theory does exert a gravitational pull on a test particle moving in its spacetime.

We derive the formulae of fluctuating hydrodynamics appropriate to a relativistically consistent divergence type theory, obtaining Landau-Lifshitz fluctuating hydrodynamics as a limiting case.

Boson stars in zero-, one- and two-node equilibrium states are modelled numerically within the framework of scalar-tensor gravity. The complex scalar field is taken to be both massive and self-interacting. Configurations are formed in the case of a linear gravitational scalar coupling (the Brans-Dicke case) and a quadratic coupling which has been used previously in a cosmological context. The coupling parameters and asymptotic value for the gravitational scalar field are chosen so that the known observational constraints on scalar-tensor gravity are satisfied. It is found that the constraints are so restrictive that the field equations of general relativity and scalar-tensor gravity yield virtually identical solutions. We then use catastrophe theory to determine the dynamically stable configurations. It is found that the maximum mass allowed for a stable state in scalar-tensor gravity in the present cosmological era is essentially unchanged from that of general relativity. We also construct boson star configurations appropriate to earlier cosmological eras and find that the maximum mass for stable states is smaller than that predicted by general relativity, and the more so for earlier eras. However, our results also show that if the cosmological era is early enough then only states with positive binding energy can be constructed.

We locate pairs of conjugate points on null geodesics along which there is a `barrier' of Weyl curvature. The existence of conjugate points in this case is predicted by general theorems. We also find that the same conjugate points can be obtained perturbatively off flat space, assuming the barrier to be weak. The conjugate points appear at second order in the perturbative approach. These results are relevant to the existence of singularities in the perturbative treatment of lightcone cuts of null infinity in asymptotically flat spacetimes that are close to Minkowski.

We develop and apply a fully covariant 1 + 3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities. Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations. We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues. The nonlinear vacuum Bianchi equations are shown to be invariant under covariant spatial duality rotation of the gravito-electric and gravito-magnetic tensor fields. We construct the super-energy density and super-Poynting vector of the gravitational field as natural U(1) group invariants, and derive their super-energy conservation equation. A covariant approach to gravito-electric/magnetic monopoles is also presented.

The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the spacetimes represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the `background' space is not asymptotically flat and requires `rotating' reference frames in order to fully simplify and view the behaviour of nearby test particles. The Kaigorodov spacetime, which is the simplest representative of the Siklos class, is analysed in more detail. It is argued that it may serve as a `cosmological' analogue of the well known homogeneous pp-waves in the flat universe.