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arXiv · gr-qc/9609019

2+1 Sector of 3+1 Gravity

Jerzy Lewandowski·Jacek Wiśniewski
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Abstract

The rank-2 sector of classical $3+1$ dimensional Ashtekar gravity is considered. It is found that the consistency of the evolution equations with the reality of the volume requires that the 3-surface of initial data is foliated by 2-surfaces tangent to degenerate triads. In turn, the degeneracy is preserved by the evolution. The 2-surfaces behave like $2+1$ dimensional empty spacetimes with a massless complex field propagating along each of them. The results provide some evidence for the issue of evolving a non-degenerate gravitational field into a degenerate sector of Ashtekar's phase space.

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Jerzy Lewandowski, Jacek Wiśniewski. 1996-09-09. 2+1 Sector of 3+1 Gravity. https://doi.org/10.1088/0264-9381%2F14%2F3%2F018

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