We present a classical Chern-Simons gauge theory for planar gravity coupled to point-like sources. The theory is defined in terms of flat coordinates whose relation with the space-time coordinates can be unambiguously established. Though flat, the theory is equivalent to Einstein's as can be shown in some explicit and non-trivial examples. The procedure we have developed allows us to find the space-time metric, the geodesics equations and also provides the coordinates that flatten the space-time manifold. In particular, we recover the stationary metric generated by N spinning particles and we discuss in full detail the matching conditions satisfied by the space-time coordinates that flatten the metric in the two-particle case.

Gravity in (2+1)-dimensions coupled to point - like sources: A Flat Chern-Simons gauge theory equivalent to Einstein's

GRIGNANI, Gianluca;
1992

Abstract

We present a classical Chern-Simons gauge theory for planar gravity coupled to point-like sources. The theory is defined in terms of flat coordinates whose relation with the space-time coordinates can be unambiguously established. Though flat, the theory is equivalent to Einstein's as can be shown in some explicit and non-trivial examples. The procedure we have developed allows us to find the space-time metric, the geodesics equations and also provides the coordinates that flatten the space-time manifold. In particular, we recover the stationary metric generated by N spinning particles and we discuss in full detail the matching conditions satisfied by the space-time coordinates that flatten the metric in the two-particle case.
1992
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/109139
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