On the relation between 2+1 Einstein gravity and Chern Simons theory

Details On the relation between 2+1 Einstein gravity and Chern Simons theory On the relation between 2+1 Einstein gravity and Chern Simons theory

1999-03-11

arxiv.org/abs/gr-qc/9903040v1

Class.Quant.Grav. 16 (1999) 2599-2609

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, LaTeX2e, 3 eps figures

Scientific paper

10.1088/0264-9381/16/8/303

A simple example is given to show that the gauge equivalence classes of physical states in Chern Simons theory are not in one-to-one correspondence with those of Einstein gravity in three spacetime dimensions. The two theories are therefore not equivalent. It is shown that including singular metrics into general relativity has more, and in fact a quite counter-intuitive, impact on the theory than one naively expects.

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