Hyperbolic geometry in 't Hooft's approach to (2 + 1)-dimensional gravity

Details Hyperbolic geometry in 't Hooft's approach to (2 + 1)-dimensional gravity Hyperbolic geometry in 't Hooft's approach to (2 + 1)-dimensional gravity

May 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cqgra..16.1503h&link_type=abstract

Classical and Quantum Gravity, Volume 16, Issue 5, pp. 1503-1518 (1999).

Physics

2

Scientific paper

In 't Hooft's polygon model of (2 + 1)-dimensional gravity coupled to point particles, the initial data are constrained by the vertex equations and the particle equations. We show that the constraint equations correspond to a hyperbolic geometry. In particular, we derive that the hyperbolic group of motions is the discrete analogue of the diffeomorphisms in the continuum theory. The hyperbolic model can be extended to point particles, but they spoil the gauge invariance. Using this insight we calculate consistent sets of initial data for the model.

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