112 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 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 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
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 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 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 gravitational-wave perturbations of
Einstein/scalar collapse to a black hole are treated by analogy with
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 , for natural 'coordinate' variables are given by the magnetic
part of the Weyl tensor, which can be taken as boundary
data on a final space-like hypersurface . For simplicity, we take the
data on the initial surface to be exactly spherically-symmetric. The
(large) Lorentzian proper-time interval between and ,
measured at spatial infinity, is denoted by . We follow Feynman's
prescription and rotate into the complex: , for . 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 . For
boundary data well below the Planck scale, and for a locally supersymmetric
theory, this involves only the semi-classical amplitude , where denotes the second-variation classical
action. The relations between the and natural boundary data,
involving supersymmetry, are investigated using 2-component spinor language in
terms of the Maxwell field strength and the Weyl spinor
Quantum states on supersymmetric minisuperspace with a cosmological constant
Spatially homogeneous models in quantum supergravity with a nonvanishing
cosmological constant are studied. A class of exact nontrivial solutions of the
supersymmetry and Lorentz constraints is obtained in terms of the Chern-Simons
action on the spatially homogeneous 3-manifold, both in Ashketar variables
where the solution is explicit up to reality conditions, and, more concretely,
in the tetrad-representation, where the solutions are given as integral
representations differing only by the contours of integration. In the limit of
a vanishing cosmological constant earlier exact solutions for Bianchi type IX
models in the tetrad-representation are recovered and additional asymmetric
solutions are found.Comment: 14 pages, late
Quantization of a Friedmann-Robertson-Walker model in N=1 Supergravity with Gauged Supermatter
The theory of N = 1 supergravity with gauged supermatter is studied in the
context of a k = + 1 Friedmann minisuperspace model. It is found by imposing
the Lorentz and supersymmetry constraints that there are {\seveni no} physical
states in the particular SU(2) model studied.Comment: 5 pages, Talk at the 1st Mexican School in Gravitation and
mathematical physics, Guanajuato, Mexico, December 12-16 199
Relic Radiation from an Evaporating Black Hole
We present a non-string-theoretic calculation of the microcanonical entropy
of relic integer-spin Hawking radiation -- at fixed total energy . The only
conserved macroscopic quantity is the total energy (the total energy of the
relic radiation). Data for a boundary-value approach, with massless,
integer-spin perturbations, are set on initial and final space-like
hypersurfaces. In the resulting 1-dimensional statistical-mechanics problem,
the real part of the (complex) time separation at spatial infinity, , is the variable conjugate to the total
energy. We count the number of weak-field configurations on the final
space-like hypersurface with energy . One recovers the Cardy formula and the
Bekenstein-Hawking entropy, if Re(T) is of the order of the black-hole life-
time, leading to a statistical interpretation of black-hole entropy. The
microcanonical entropy includes a logarithmic correction to the black-hole area
law, which is {\it universal} (independent of black-hole parameters). Here, the
discreteness of the energy levels is crucial. This approach is compared with
that of string theory for the transition to the fundamental-string r\'egime in
the final stages of evaporation. The squared coupling, , regulating the
transition to a highly-excited string state and {\it vice versa}, can be
related to the angle, , of complex-time rotation above. The
strong-coupling r\'egime corresponds to a Euclidean black hole, while the
physical limit of a Lorentzian space-time (as ) corresponds to
the weak-coupling r\'egime. This resembles the transition to a highly-excited
string-like state which subsequently decays into massless particles, thereby
avoiding the naked singularity.Comment: To appear in International Journal of Modern Physics
No Quantum Super-Minisuperspace with
We show that the quantum super-minisuperspace of N=1 supergravity with
has no non-trivial physical states for class A Bianchi models.
Hence, in super quantum cosmology, the vanishing of is a condition
for the existence of the universe. We argue that this result implies that in
full supergravity with there are no non-trivial physical states with
a finite number of fermionic fields. We use the Jacobson canonical formulation.Comment: 9 pages, LaTeX, CIEA-94-0
Planckian Energy Scattering and Surface Terms in the Gravitational Action
This is a revised version of our previous paper by the same name and preprint
number. It contains various changes, two figures and new results in sect.5. We
propose a new approach to four-dimensional Planckian-energy scattering in which
the phase of the -matrix is written---to leading order in and
to all orders in ---in terms of the surface term of the gravity
action and of a boundary term for the colliding quanta. The proposal is checked
at the leading order in and also against some known examples of
scattering in strong gravitational fields.Comment: preprint CERN-TH.6904/93/rev (Latex file, 46 pages, 2 figures not
included
Is there a problem with quantum wormhole states in N=1 Supergravity?
The issue concerning the existence of wormhole states in locally
supersymmetric minisuperspace models with matter is addressed. Wormhole states
are apparently absent in models obtained from the more general theory of N=1
supergravity with supermatter. A Hartle-Hawking type solution can be found,
even though some terms (which are scalar field dependent) cannot be determined
in a satisfactory way. A possible cause is investigated here. As far as the
wormhole situation is concerned, we argue here that the type of Lagrange
multipliers and fermionic derivative ordering used can make a difference. A
proposal is made for supersymmetric quantum wormholes to also be invested with
a Hilbert space structure, associated with a maximal analytical extension of
the corresponding minisuperspace.is concerned, we argue here that the type of
Lagrange multipliers and fermionic derivative ordering used can make a
difference. A proposal is made for supersymmetric quantum wormholes to also be
invested with a Hilbert space structure, associated with a maximal analytical
extension of the corresponding minisuperspace.Comment: 22 pages, TeX (some font problems may occur, just press Return),
Based on a essay submitted to the 1995 ravity Research Foundation Awards,
accepted in G.R.
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