90 research outputs found

### 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

### Spin-2 Amplitudes in Black-Hole Evaporation

Quantum amplitudes for $s=2$ gravitational-wave perturbations of
Einstein/scalar collapse to a black hole are treated by analogy with $s=1$
Maxwell perturbations. The spin-2 perturbations split into parts with odd and
even parity. We use the Regge-Wheeler gauge; at a certain point we make a gauge
transformation to an asymptotically-flat gauge, such that the metric
perturbations have the expected falloff behaviour at large radii. By analogy
with $s=1$, for $s=2$ natural 'coordinate' variables are given by the magnetic
part $H_{ij} (i,j=1,2,3)$ of the Weyl tensor, which can be taken as boundary
data on a final space-like hypersurface $\Sigma_F$. For simplicity, we take the
data on the initial surface $\Sigma_I$ to be exactly spherically-symmetric. The
(large) Lorentzian proper-time interval between $\Sigma_I$ and $\Sigma_F$,
measured at spatial infinity, is denoted by $T$. We follow Feynman's
$+i\epsilon$ prescription and rotate $T$ into the complex: $T\to{\mid}T{\mid}
\exp(-i\theta)$, for $0<\theta\leq\pi/2$. The corresponding complexified {\it
classical} boundary-value problem is expected to be well-posed. The Lorentzian
quantum amplitude is recovered by taking the limit as $\theta\to 0_+$. For
boundary data well below the Planck scale, and for a locally supersymmetric
theory, this involves only the semi-classical amplitude $\exp(iS^{(2)}_{\rm
class}$, where $S^{(2)}_{\rm class}$ denotes the second-variation classical
action. The relations between the $s=1$ and $s=2$ natural boundary data,
involving supersymmetry, are investigated using 2-component spinor language in
terms of the Maxwell field strength $\phi_{AB}=\phi_{(AB)}$ and the Weyl spinor
$\Psi_{ABCD}=\Psi_{(ABCD)}$

### 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

### 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.

- …