Table of contents

Two-dimensional supergravity is shown to be related to the Osp(¹/₂) WZWN model.

The renormalization procedure for the classical bosonic string coupled to the massless scalar field has been carried out. It has been established that the classical equations of motion for this system are nonrenormalizable if the number of spacetime dimensions D exceeds four. The results of the analysis indicate that all of the string excitation modes must be included in order to make the string a finite object.

It is shown that all known formulations of N=1 superparticle dynamics in D=2, 3, 4 and 6 spacetime dimensions as double supersymmetric theories with n=D-2 local worldline superconformal symmetries are particular versions of more general n=D-2 superfield action, which is invariant under generalized (superfield) kappa -symmetry and coincides (on shell) with the Brink-Schwarz superparticle action.

The solutions to the duality equations for the blown-up orbifold are studied. In particular the possibility of having the prepotential completely determined by the Yukawa couplings is analysed in detail.

For pt. I see ibid., vol.10, p.631 (1993). The solutions to the duality equations for the blown-up orbifold are studied. In particular the possibility of having the prepotential completely determined by the Yukawa couplings is analysed in detail.

In the loop representation of quantum gravity in 3+1 dimensions, there is a space of physical states consisting of invariants of links in S³. The correct inner product on this space of states is not known, or in other words, the *-algebra structure of the algebra of observables has not been determined. In order to address this issue, the author works instead with quantum gravity on D³, and work with a space K spanned by tangles. A certain algebra T, the 'tangle algebra', acts as operators on K. The 'empty link' psi ₀, corresponding to the class of the empty set, is shown to be a cyclic vector for T. The author constructs inner products on quotients of K from link invariants, shows that these quotients are representations of T, and calculates the *-algebra structures of T in these representations. In particular, taking the link invariant to be the Jones polynomial (or more precisely, Kauffman bracket), the author obtains the inner product for states of quantum gravity arising from SU(2) Chern-Simons theory.

Previously, various examples of topology changing processes by quantum tunnelling were demonstrated in the WKB approximation in (2+1)-dimensional Einstein gravity with negative cosmological constant. The authors explicitly show a specific continuation of the Euclidean metric to the Lorentzian signature region.

Extending the proof of the cosmic no-hair theorem for Bianchi models in power-law inflation, the authors prove a more general cosmic no-hair theorem for all 0<or= lambda < square root 2, where lambda is the coupling constant of an exponential potential of an inflaton phi , exp(- lambda kappa phi ). For any initially expanding Bianchi-type model except type IX, they find that the isotropic inflationary solution is the unique attractor and that anisotropies always enhance inflation. For Bianchi IX, this conclusion is also true, if the initial ratio of the vacuum energy Lambda _eff to the maximum 3-curvature ⁽³⁾R_max is larger than 1/(3(1- lambda ²/2)) and its time derivative is initially positive. It turns out that the sufficient condition for inflation in Bianchi type=IX spacetimes with cosmological constant Lambda , which is a special case of the theorem ( lambda =0) become less restrictive than Wald's one (1984). For type IX, they also show a recollapse theorem.

The phase-integral method has proved to be a powerful tool for studying the quasinormal modes of black holes. A generalization of the WKB methods of quantum mechanics, its treatment of the complex coordinate plane brings a number of important simplifications and potentially powerful computational aids to bear on the problem of computing eigenfrequencies with large imaginary parts. It holds great promise of further applications to related problems, such as the quasinormal modes of relativistic stars. However, in some respects the method is incomplete, particularly in its assessment of error bounds. The authors make available to researchers in the field of relativity a simple and self-contained introduction to the fundamental concepts of the phase-integral method, in which they also point out areas that seem to need further development. As an example of the use of the method, they derive the two-transition-point phase-integral formula for quasinormal modes of the Schwarzschild black hole, which is an accurate asymptotic approximation for the first modes. They provide the foundation for related papers in which they use the method to develop accurate asymptotic expressions for highly damped modes.

A generalized Bohr-Sommerfeld-type formula determining the quasinormal-mode frequencies of Schwarzschild black holes is derived using the phase-integral method with three transition points. The formula is valid provided that these points are well separated from each other, and is remarkably accurate for the high-overtone modes. It makes a great improvement over the conventional Bohr-Sommerfeld formula, derived from two transition points.

The puzzling possibility of a nonequilibrium fluid to evolve reversibly (i.e. with vanishing rate of entropy production), provided it flows along a conformal Killing vector field of a background spacetime, is examined. A hypothetical example in a Robertson-Walker geometry is furnished.

On a null 3-surface, the general solution to the vacuum Einstein equations is found in closed form in terms of free initial data. The solution is valid up to caustics, whose occurrence is determined by a necessary and sufficient condition on the initial data.

The Einstein gravitational field is decomposed with respect to two intersecting foliations of null surfaces. The dynamics are cast in the form of suitably generalized Lagrangian and Hamiltonian theories. The vacuum Einstein equations are written in terms of geometrical fields and operators adapted to the null foliations. There are no constraints. The free initial data are identified.

The author proves the staticity and no-hair conjectures for self-gravitating nonlinear sigma -models with Riemannian target manifolds. The author first demonstrates that any self-coupled, stationary scalar mapping ( sigma -model) from a strictly stationary domain of outer communications with nonrotating horizon to a Riemannian manifold has to be static. Applying the positive mass theorem, the author subsequently shows that the exterior Schwarzschild geometry is the only maximally extended, static, asymptotically flat solution of the coupled Einstein- sigma -model equations with regular (but not necessarily connected) horizon.

The discrete series of SU(2)-Einstein-Yang-Mills fields of Bartnik and McKinnon (1988) also provides an example of finite-energy pure YM fields on an asymptotically flat Riemannian 3-manifold. The authors explain why this does not contradict Deser's nonexistence theorem (1984).

The Hamiltonian formulation of general relativity may be described in an extended framework in terms of Ashtekar's variables. In this framework degenerate triads are allowed as solutions of the constraint equations. The author shows that for degenerate triads, the reality conditions imply, in general, one nontrivial relation which involves only triads, and which has to be considered in addition to the constraints.

Analysis of the most general laser interferometer gravitational detectors (LIGDs) are given in terms of the scattering parameters of the individual components. Each arm of the interferometer may contain a number of lossy, partially reflecting, reciprocal or nonreciprocal components or layers, forming a complex cavity. Similarly the beamsplitter can introduce a partial scattering of the incident light from any surface to any arm of the interferometer. The method is applied to the previously analysed dual and compound recycling interferometers, as illustrative examples. In the previous works it is generally assumed that the so-called power and signal recycling circuits are decoupled. This is only true if, in the absence of the gravitational field, the light from the two main arms of the interferometer entering the detector arm is totally cancelled. This assumption need not be made. The effect of any derivation from the null condition can hence be easily studied. Birefringence is not considered, but the analysis can easily be extended to include the birefringence in the beamsplitter or polarization effects of other components.