Table of contents

We consider relativistic and non-relativistic particles and strings in spaces (or spacetimes) with a degenerate metric. We show that the resulting dynamics is described by a rich structure of constraints. All constraints are classified and the dynamics depends strongly on the parity of the difference between the dimension of the space (or spacetime) and the rank of the degenerate metric. For a particular class of degenerate metrics we can use the null eigenvectors of the metric in order to obtain an isometry condition. We also give the first steps towards the quantization of the non-relativistic particle using the Senjanovic path integral quantization and the Batalin-Fradkin-Tyutin conversion method.

We formulate the field equations for SU ( ) Einstein-Yang-Mills theory, and use an analytic approximation to elucidate the properties of spherically symmetric black hole solutions. This model may be motivated by string theory considerations, given the enormous gauge symmetries which characterize string theory. The solutions simplify considerably in the presence of a negative cosmological constant, particularly for the limiting cases of a very large cosmological constant or very small gauge field. The black holes possess infinite amounts of gauge field hair, and we speculate on possible consequences of this for quantum decoherence, which, however, we do not tackle here.

We study the class of Lemos-Letelier annular discs (realistic gravitating static axisymmetric thin discs obtained by inversion of the first Morgan-Morgan solution) around Schwarzschild black holes. For each value of the inner radius, the range of masses is found when all of the disc can be interpreted by counter-rotating streams of particles on stable timelike geodesics. One can then consider a sequence of stable physical discs with different masses and inner rims at the corresponding least possible radii. The basic properties of this sequence are shown on positions of the inner rims and of important circular orbits, on positions of the horizon and on density and Keplerian-velocity profiles within the discs, plotted in terms of the Schwarzschild radial coordinate, circumferential radius and proper distance from the horizon.

We construct non-standard interactions between exterior form gauge fields by gauging a particular global symmetry of the Einstein-Maxwell action for such fields. Furthermore, we discuss generalizations of such interactions by adding couplings to gravitational Chern-Simons forms and to fields arising through dimensional reduction. The construction uses an appropriate tensor calculus.

An embedding diagram helps visualize the observer-dependent projected spatial geometry of the equatorial plane in the Kerr spacetime as seen by a family of circularly rotating observers. This is described for the various geometrically defined families of such observers, motivated by the attempt to better understand how the spatial geometry contributes to the properties of particle motion as seen by those observers. A new family of observers is introduced for which the equatorial plane appears to be flat.

A model for two-dimensional (2D) quantum gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c , some quantum operators (SL (2, ) generators) lose their dynamical content (they are no longer conjugated operators). The notion of spacetime itself in 2D gravity then arises as associated with this kinematical SL (2, ) symmetry. An ensemble of different copies of AdS do co-exist in this model with different weights, depending on their curvature (which is proportional to ² ) and they are connected by gravity operators. This model suggests that, in general, quantum diffeomorphisms should not be imposed as constraints to the theory, except for the classical limit.

The dynamics of the hyperextended scalar-tensor theory in the empty Bianchi type I model is investigated. We describe a method giving the sign of the first and second derivatives of the metric functions whatever the coupling function. Hence, we can predict whether a theory gives birth to an expanding, contracting, bouncing or inflationary cosmology. The dynamics of a string-inspired theory without an antisymmetric field strength is analysed. Some exact solutions are found.

A generalized Lie derivative operator suitable for use within the GHP formalism and the notion of preferred GHP tetrads relative to a vector are introduced. The usual homothetic or Killing equations are then replaced by an equivalent but much more manageable set of equations involving the commutators of this new operator with the four GHP derivative operators. This allows for an efficient treatment of the homothetic or Killing condition when constructing new solutions of Einstein's field equations or when obtaining the homothetic and/or Killing vectors for a given metric. Two applications are given. The first sheds new light on the vacuum twisting type N problem with one or two homothetic/Killing vectors. In the second we find the subclass of all type N, and of all conformally flat, pure radiation metrics (with 0) which possess one or more homothetic or Killing vectors.

We investigate the hypothesis that the scalar field is the dark matter and the dark energy in the cosmos, which comprises about 95% of the matter of the Universe. We show that this hypothesis explains quite well the recent observations on type Ia supernovae.

We describe a simple method for generating new string solutions for which the brane worldvolume is a curved space. As a starting point we use solutions with NS-NS charges combined with two-dimensional CFTs representing different parts of spacetime. We illustrate our method with many examples, some of which are associated with conformally invariant sigma models. Using U-duality, we also obtain supergravity solutions with RR charges which can be interpreted as D-branes with non-trivial worldvolume geometry. In particular, we discuss the case of a D5-brane wrapped on AdS₃× S³ , a solution interpolating between AdS₃× S³× ⁵and AdS₃× S³× S³× , and a D3-brane wrapped over S³× or AdS₂× S² . Another class of solutions we discuss involves NS5-branes intersecting over a 3-space and NS5-branes intersecting over a line. These solutions are similar to D7-brane or cosmic string backgrounds.

In a recent paper by Liu and Wesson (Liu H and Wesson P S 1997 Class. Quantum Grav.141651) an analysis was made of a 5D general relativity (GR) (Kaluza-Klein-type) metric representing a charge distribution. In their analysis, they stated that the equation of state represented by their metric was that of radiation. Here, I comment on an error in that analysis, showing that the equation of state is not, in fact, that of radiation. As it turns out, this works to the metric's advantage.