Table of contents

We study the quantum cosmology of a five-dimensional non-compactified Kaluza-Klein theory where the four-dimensional (4D) metric depends on the fifth coordinate, x⁴≡l. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l = constant by the extra coordinate dependence in the four-dimensional metric. We show that the Vilenkin wavefunction of the universe is more convenient for this model as it predicts a newborn 4D universe on the l≃0 constant hypersurface.

The convergence of polyhomogeneous expansions of zero-rest-mass fields in asymptotically flat spacetimes is discussed. An existence proof for the asymptotic characteristic initial-value problem for a zero-rest-mass field with polyhomogeneous initial data is given. It is shown how this non-regular problem can be properly recast as a set of regular initial-value problems for some auxiliary fields. The standard techniques of symmetric hyperbolic systems can be applied to these new auxiliary problems, thus yielding a positive answer to the question of existence in the original problem.

The causal relation K⁺ was introduced by Sorkin and Woolgar to extend the standard causal analysis of C² spacetimes to those that are only C⁰. Most of their results also hold true in the case of metrics with degeneracies which are C⁰ but vanish at isolated points. In this paper we seek to examine K⁺ explicitly in the case of topology-changing `Morse histories' which contain degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that K⁺ is robust and the Hawking and Sachs characterization of causal continuity translates into a natural condition in terms of K⁺. We then examine K⁺ in topology-changing Morse spacetimes with the degenerate points excised and then for the Morse histories in which the degenerate points are reinstated. We find further characterizations of causal continuity in these cases.

Within the framework of the Penrose conformal approach to asymptotical flatness we find minimal conditions on the Ricci tensor of the physical metric which guarantee that the Bondi mass and momentum are well defined. The energy-momentum vector, the Bondi news functions and the energy loss formula are expressed in terms of the Penrose conformal factor. An approximate Bondi-Sachs form of the metric is constructed. The Robinson-Trautman metrics are considered as an example.

We present a calculation of the maximum sensitivity achievable by the LIGO gravitational wave detector in construction, due to limiting thermal noise of its suspensions. We present a method to calculate thermal noise that allows the prediction of the suspension thermal noise in all of its six degrees of freedom, from the energy dissipation due to the elasticity of the suspension wires. We show how this approach encompasses and explains previous ways to approximate the thermal noise limit in gravitational wave detectors. We show how this approach can be extended to more complicated suspensions to be used in future LIGO detectors.

Within the framework of a five-dimensional model with one 3-brane and an infinite extra dimension, we discuss a process in which matter escapes from the brane and propagates into the bulk to arbitrarily large distances. An example is a decay of a particle of mass 2m residing on the brane into two particles of mass m that leave the brane and accelerate away. We calculate, in the linearized theory, the metric induced by these particles on the brane. This metric does not obey the four-dimensional Einstein equations and corresponds to a spherical gravity wave propagating along the four-dimensional future lightcone. The four-dimensional spacetime left behind the spherical wave is flat, so the gravitational field induced in the brane world by matter escaping from the brane disappears in a causal way.

The most general theory of gravity in d dimensions which leads to second-order field equations for the metric has [(d-1)/2] free parameters. It is shown that requiring the theory to have the maximum possible number of degrees of freedom, fixes these parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chern-Simons form for the (A)dS or Poincaré groups. In even dimensions, the action has a Born-Infeld-like form.

Torsion may occur explicitly in the Lagrangian in the odd-parity sector and the torsional pieces respect local (A)dS symmetry for d = 4k-1 only. These torsional Lagrangians are related to the Chern-Pontryagin characters for the (A)dS group. The additional coefficients in front of these new terms in the Lagrangian are shown to be quantized.

We investigated the evolution of the primordial density perturbations produced by inflation with thermal dissipation. A full relativistic analysis on the evolution of initial perturbations from the warm inflation era to a radiation-dominated universe has been developed. The emphasis is on tracking the ratio between the adiabatic and the isocurvature mode of the initial perturbations. This result is employed to calculate a testable factor: the super-Hubble suppression of the power spectrum of the primordial perturbations. We show that based on the warm inflation scenario, the super-Hubble suppression factor, s, for an inflation with thermal dissipation is at least 0.5. This prediction does not depend on the details of the model parameters. If s is larger than 0.5, it implies that the friction parameter Γ is larger than the Hubble expansion parameter H during the inflation era.

With the aim of testing the cosmic censorship conjecture for perfect fluid spacetimes, two classes of spherically symmetric perfect fluid solutions obeying the shear-free condition are examined. The final end states of gravitational collapse can be investigated analytically for such solutions, and it is shown that homogeneous configurations always form black holes. This property also holds true for inhomogeneous solutions provided that the collapse occurs in a synchronous manner.

The non-commutative geometry is a possible framework to regularize quantum field theory in a non-perturbative way. This idea is an extension of the lattice approximation by non-commutativity that allows us to preserve symmetries. The supersymmetric version is also studied and more precisely in the case of the Schwinger model on a supersphere. This paper is a generalization of this latter work to more general gauge groups.

We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization approach based on Ashtekar's new variables and spin networks. With this approach one can find perturbatively classical observables (quantities that have vanishing Poisson brackets with the constraints) and quantum states (states that are annihilated by the quantum constraints). The relative ease with which the technique appears to deal with these traditionally hard problems opens up several questions concerning how relevant the results produced can possibly be. Among the questions is the issue of how useful are results for large values of the cosmological constant and how the approach can deal with several pathologies that are expected to be present in the canonical approach to quantum gravity. With the aim of clarifying these points, and to make our construction as explicit as possible, we study its application in several simple models. We consider Bianchi cosmologies, the asymmetric top, coupled harmonic oscillators with constant energy density and a simple quantum mechanical system with two Hamiltonian constraints. We find that the technique satisfactorily deals with the pathologies of these models and offers promise for finding (at least some) results even for small values of the cosmological constant. Finally, we briefly sketch how the method would operate in the full four-dimensional quantum general relativity case.

Discussion of the equatorial photon motion in Kerr-Newman black-hole and naked-singularity spacetimes with a non-zero cosmological constant is presented. Both repulsive and attractive cosmological constants are considered. An appropriate `effective potential' governing the photon radial motion is defined, circular photon orbits are determined, and their stability with respect to radial perturbations is established. The spacetimes are divided into separated classes according to the properties of the `effective potential'. There is a special class of Kerr-Newman-de Sitter black-hole spacetimes with the restricted repulsive barrier. In such spacetimes, photons with high positive and all negative values of their impact parameter can travel freely between the outer black-hole horizon and the cosmological horizon due to an interplay between the rotation of the source and the cosmological repulsion. It is shown that this type of behaviour of the photon motion is connected to an unusual relation between the values of the impact parameters of the photons and their directional angles relative to the outward radial direction as measured in the locally non-rotating frames. Surprisingly, some photons counterrotating in these frames have a positive impact parameter. Such photons can be both escaping or captured in the black-hole spacetimes with the restricted repulsive barrier. For the black-hole spacetimes with a standard, divergent repulsive barrier of the equatorial photon motion, the counterrotating photons with positive impact parameters must all be captured from the region near the black-hole outer horizon as in the case of Kerr black holes, while they all escape from the region near the cosmological horizon. Further, the azimuthal motion is discussed and photon trajectories are given in typical situations. It is shown that for some photons with negative impact parameter turning points of their azimuthal motion can exist.

We present a proof of the positivity of the Bondi energy in Einstein-Maxwell axion dilaton gravity, being the low-energy limit of the heterotic string theory. We consider the spacelike hypersurface which asymptotically approaches a null cone and on which the equations of the theory under consideration are given. Next, we generalize the proof allowing the hypersurface having inner boundaries.

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two non-commuting Killing vectors. We study the case when the homothetic parameter ϕ takes the value -1, which is shown to admit a reduction to a third-order real ordinary differential equation for this problem, similar to that previously obtained by one of us when two Killing vectors are present.