Physical states in N=1N = 1 supergravity

By solving the supersymmetry constraints for physical wave-functions, it is shown that the only two allowed bosonic states in $N = 1$ supergravity are of the form const.~exp~$(\pm I / \hbar)$, where $I$ is an action functional of the three-metric. States containing a finite number of fermions are forbidden. In the case that the spatial topology is $S^3$, the state const.~exp~$(- I / \hbar)$ is the wormhole ground state, and the state const.~exp~$(I / \hbar)$ is the Hartle--Hawking state. $N = 1$ supergravity has no quantum ultraviolet divergences, and no quantum corrections.Comment: 9 pages, DAMTP Preprint DAMTP-R-93-

Supersymmetric Bianchi class A models

The canonical theory of $N=1$ supergravity is applied to Bianchi class A spatially homogeneous cosmologies. The full set of quantum constraints are then solved with the possible ordering ambiguity taken into account by introducing a free parameter. The wave functions are explicitly given for all the Bianchi class A models in a unified way. Some comments are made on the Bianchi type IX cases.Comment: 9 pages, LaTeX, TIT/HEP-221/COSMO-3

Physical States in Canonically Quantized Supergravity

We discuss the canonical quantization of $N=1$ supergravity in the functional Schrodinger representation. Although the form of the supersymmetry constraints suggests that there are solutions of definite order $n$ in the fermion fields, we show that there are no such states for any finite $n$. For $n=0$, a simple scaling argument definitively excludes the purely bosonic states discussed by D'Eath. For $n>0$, the argument is based on a mode expansion of the gravitino field on the quantization 3-surface. It is thus suggested that physical states in supergravity have infinite Grassmann number. This is confirmed for the free spin-3/2 field, for which we find that states satisfying the gauge constraints contain an infinite product of fermion mode operators.Comment: 36 pages (uses jnl.tex), CTP #227

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

Bogoliubov transformations for amplitudes in black-hole evaporation

The familiar approach to quantum radiation following collapse to a black hole proceeds via Bogoliubov transformations, and yields probabilities for final outcomes. In our (complex) approach, we find quantum amplitudes, not just probabilities, by following Feynman's $+i\epsilon$ prescription. Initial and final data for Einstein gravity and (say) a massless scalar field are specified on a pair of asymptotically-flat space-like hypersurfaces $\Sigma_I$ and $\Sigma_F$; both are diffeomorphic to ${\Bbb R}^3$. Denote by $T$ the (real) Lorentzian proper-time interval between the surfaces, as measured at spatial infinity. Then rotate: $T\to{\mid}T{\mid}\exp(-i\theta),0<\theta\leq \pi/2$. The {\it classical} boundary-value problem is expected to be well-posed on a region of topology $I\times{\Bbb R}^3$, where $I$ is a closed interval. For a locally-supersymmetric theory, the quantum amplitude should be dominated by the semi-classical expression $\exp(iS_{\rm class})$, where $S_{\rm class}$ is the classical action. One finds the Lorentzian quantum amplitude from the limit $\theta\to 0_+$. In the usual approach, the only possible such final surfaces are in the strong-field region shortly before the curvature singularity. In our approach one can put arbitrary smooth gravitational data on $\Sigma_F$, provided that it has the correct mass $M$ -- the singularity is by-passed in the analytic continuation. Here, we consider Bogoliubov transformations and their possible relation to the probability distribution and density matrix in the traditional approach. We find that our probability distribution for configurations of the final scalar field cannot be expressed in terms of the diagonal elements of some non-trivial density-matrix distribution

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

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

Continuous coordinates for all impulsive pp - waves

We present a coordinate system for a general impulsive gravitational pp - wave in vacuum in which the metric is explicitly continuous, synchronous and "transverse". Also, it is more appropriate for investigation of particle motions.Comment: 4 pages, LaTeX, no figures, to be published in Phys. Lett.

Gravitational radiation from collisions at the speed of light: a massless particle falling into a Schwarzschild black hole

We compute spectra, waveforms, angular distribution and total gravitational energy of the gravitiational radiation emitted during the radial infall of a massless particle into a Schwarzschild black hole. Our fully relativistic approach shows that (i) less than 50% of the total energy radiated to infinity is carried by quadrupole waves, (ii) the spectra is flat, and (iii) the zero frequency limit agrees extremely well with a prediction by Smarr. This process may be looked at as the limiting case of collisions between massive particles traveling at nearly the speed of light, by identifying the energy $E$ of the massless particle with $m_0 \gamma$, $m_0$ being the mass of the test particle and $\gamma$ the Lorentz boost parameter. We comment on the implications for the two black hole collision at nearly the speed of light process, where we obtain a 13.3% wave generation efficiency, and compare our results with previous results by D'Eath and Payne.Comment: 10 pages, 3 figures, published versio