Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry

Details Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry

2010-12-08

arxiv.org/abs/1012.1835v2

Class.Quant.Grav.28:125008,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

44 pages, 7 figures; v2 makes a few small improvements suggested by referees

Scientific paper

10.1088/0264-9381/28/12/125008

We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space. The chosen gauge fixing conditions have a natural physical interpretation and specify an observer in the spacetime. We derive explicit expressions for the resulting Dirac brackets and discuss their geometrical interpretation. In particular, we show that specifying an observer with respect to two point particles gives rise to conical spacetimes, whose deficit angle and time shift are determined, respectively, by the relative velocity and minimal distance of the two particles.

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