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ID: 342062.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Null-Killing vector dimensional reduction and Galilean geometrodynamics
Authors:Julia, Bernard; Nicolai, Hermann
Date of Publication (YYYY-MM-DD):1995-04
Title of Journal:Nuclear Physics B
Issue / Number:1-2
Start Page:291
End Page:326
Review Status:not specified
Audience:Not Specified
Abstract / Description:The solutions of Einstein's equations admitting one non-null Killing vector field are best studied with the projection formalism of Geroch. When the Killing vector is lightlike, the projection onto the orbit space still exists and one expects a covariant theory with degenerate contravariant metric to appear, its geometry is presented here. Despite the complications of indecomposable representations of the local Euclidean subgroup, one obtains an absolute time and a canonical, Galilean and so-called Newtonian, torsionless connection. The quasi-Maxwell field (Kaluza Klein one-form) that appears in the dimensional reduction is a non-separable part of this affine connection, in contrast to the reduction with a non-null Killing vector. One may define the Kaluza Klein scalar (dilaton) together with the absolute time coordinate after having imposed one of the equations of motion in order to prevent the emergence of torsion. We present a detailed analysis of the dimensional reduction using moving frames, we derive the complete equations of motion and propose an action whose variation gives rise to all but one of them. Hidden symmetries are shown to act on the space of solutions.
External Publication Status:published
Document Type:Article
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
External Affiliations:Institute for Theoretical Physics, Hamburg University, Luruper Chaussee 149, Hamburg 22761, Germany
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