Quantization of the Bianchi type-IX model in supergravity with a cosmological constant

Diagonal Bianchi type-IX models are studied in the quantum theory of $N = 1$ supergravity with a cosmological constant. It is shown, by imposing the supersymmetry and Lorentz quantum constraints, that there are no physical quantum states in this model. The $k = + 1$ Friedmann model in supergravity with cosmological constant does admit quantum states. However, the Bianchi type-IX model provides a better guide to the behaviour of a generic state, since more gravitino modes are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N = 1$ supergravity with a non-zero cosmological constant. are available to be excited. These results indicate that there may be no physical quantum states in the full theory of $N = 1$ supergravity with a non-zero cosmological constant.Comment: 17 pages report DAMTP R93/3

Diagonal quantum Bianchi type IX models in N=1 supergravity

We take the general quantum constraints of N=1 supergravity in the special case of a Bianchi metric, with gravitino fields constant in the invariant basis. We construct the most general possible wave function which solves the Lorentz constraints and study the supersymmetry constraints in the Bianchi Class A Models. For the Bianchi-IX cases, both the Hartle-Hawking state and wormhole state are found to exist in the middle fermion levels.Comment: plain LaTex, 17 pages, accepted for publication in Classical Quantum Gravit

Supersymmetric minisuperspace with non-vanishing fermion number

The Lagrangean of $N=1$ supergravity is dimensionally reduced to one (time-like) dimension assuming spatial homogeneity of any Bianchi type within class A of the classification of Ellis and McCallum. The algebra of the supersymmetry generators, the Lorentz generators, the diffeomorphism generators and the Hamiltonian generator is determined and found to close. In contrast to earlier work, infinitely many physical states with non-vanishing even fermion number are found to exist in these models, indicating that minisuperspace models in supergravity may be just as useful as in pure gravity.Comment: 4 page

Constructing Time Machines

The existence of time machines, understood as spacetime constructions exhibiting physically realised closed timelike curves (CTCs), would raise fundamental problems with causality and challenge our current understanding of classical and quantum theories of gravity. In this paper, we investigate three proposals for time machines which share some common features: cosmic strings in relative motion, where the conical spacetime appears to allow CTCs; colliding gravitational shock waves, which in Aichelburg-Sexl coordinates imply discontinuous geodesics; and the superluminal propagation of light in gravitational radiation metrics in a modified electrodynamics featuring violations of the strong equivalence principle. While we show that ultimately none of these constructions creates a working time machine, their study illustrates the subtle levels at which causal self-consistency imposes itself, and we consider what intuition can be drawn from these examples for future theories.Comment: 36 pages, 14 figures, TeX with harvmac; Review article prepared for Int. J. Mod. Phys.

Gravitational Shock Waves for Schwarzschild and Kerr Black Holes

The metrics of gravitational shock waves for a Schwarzschild black hole in ordinary coordinates and for a Kerr black hole in Boyer-Lindquist coordinates are derived. The Kerr metric is discussed for two cases: the case of a Kerr black hole moving parallel to the rotational axis, and moving perpendicular to the rotational axis. Then, two properties from the derived metrics are investigated: the shift of a null coordinate and the refraction angle crossing the gravitational shock wave. Astrophysical applications for these metrics are discussed in short.Comment: 24 Pages, KOBE--FHD--93--03, {\LaTeX