28 research outputs found
A Periodic Analog of the Schwarzschild Solution
We construct a new exact solution of Einstein's equations in vacuo in terms
of Weyl canonical coordinates. This solution may be interpreted as a black hole
in a space-time which is periodic in one direction and which behaves
asymptotically like the Kasner solution with Kasner index equal to ,
where is the period and is the mass of the black hole. Outside the
horizon, the solution is free of singularities and approaches the Schwarzschild
solution as .Comment: 6 pages, preprint DESY-TH 94-03
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of
dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space
sigma-models coupled to gravity and a dilaton. Using methods developed in the
context of flat space integrable systems, the Wheeler-DeWitt equations for
these models can be reduced to a modified version of the Knizhnik-Zamolodchikov
equations from conformal field theory, the insertions given by singularities in
the spectral parameter plane. This basic result in principle permits the
explicit construction of solutions, i.e. physical states of the quantized
theory. In this way, we arrive at integrable models of quantum gravity with
infinitely many self-interacting propagating degrees of freedom.Comment: 41 pages, 2 figures, Lectures given at NATO Advanced Study Institute
on Quantum Fields and Quantum Space Time, Cargese, France, 22 July - 3 Augus
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom
On quantum gravity coupled to a \s-model
This contribution is a review of the method of isomonodromic quantization of
dimensionally reduced gravity. Our approach is based on the complete separation
of variables in the isomonodromic sector of the model and the related
``two-time" Hamiltonian structure. This allows an exact quantization in the
spirit of the scheme developed in the framework of integrable systems. Possible
ways to identify a quantum state corresponding to the Kerr black hole are
discussed. In addition, we briefly describe the relation of this model with
Chern Simons theory.Comment: 9 pages, LaTeX style espcrc2, to appear in Proceedings of 29th
International Symposium Ahrenshoop, Buckow, 199
An Integrable Model of Quantum Gravity
We present a new quantization scheme for gravity coupled to an
principal chiral field and a dilaton; this model represents a slightly
simplified version of stationary axisymmetric quantum gravity. The analysis
makes use of the separation of variables found in our previous work [1] and is
based on a two-time hamiltonian approach. The quantum constraints are shown to
reduce to a pair of compatible first order equations, with the dilaton playing
the role of a ``clock field''. Exact solutions of the Wheeler-DeWitt equation
are constructed via the integral formula for solutions of the
Knizhnik-Zamolodchiokov equations.Comment: 12 page
Isomonodromic Quantization of Dimensionally Reduced Gravity
We present a detailed account of the isomonodromic quantization of
dimensionally reduced Einstein gravity with two commuting Killing vectors. This
theory constitutes an integrable ``midi-superspace" version of quantum gravity
with infinitely many interacting physical degrees of freedom. The canonical
treatment is based on the complete separation of variables in the isomonodromic
sectors of the model. The Wheeler-DeWitt and diffeomorphism constraints are
thereby reduced to the Knizhnik-Zamolodchikov equations for . The
physical states are shown to live in a well defined Hilbert space and are
manifestly invariant under the full diffeomorphism group. An infinite set of
independent observables \`a la Dirac exists both at the classical and the
quantum level. Using the discrete unitary representations of , we
construct explicit quantum states. However, satisfying the additional
constraints associated with the coset space requires solutions
based on the principal series representations, which are not yet known. We
briefly discuss the possible implications of our results for string theory.Comment: 36 pages, LATE
The Ernst Equation on a Riemann Surface
The Ernst equation is formulated on an arbitrary Riemann surface.
Analytically, the problem reduces to finding solutions of the ordinary Ernst
equation which are periodic along the symmetry axis. The family of (punctured)
Riemann surfaces admitting a non-trivial Ernst field constitutes a ``partially
discretized'' subspace of the usual moduli space. The method allows us to
construct new exact solutions of Einstein's equations in vacuo with non-trivial
topology, such that different ``universes'', each of which may have several
black holes on its symmetry axis, are connected through necks bounded by cosmic
strings. We show how the extra topological degrees of freedom may lead to an
extension of the Geroch group and discuss possible applications to string
theory.Comment: 22 page