Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-07-22
Int.J.Mod.Phys. A16 (2001) 2817-2839
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, no figures, LaTeX file
Scientific paper
10.1142/S0217751X01004220
We discuss a formalism for solving (2+1) AdS gravity on Riemann surfaces. In the torus case the equations of motion are solved by two functions f and g, solutions of two independent O(2,1) sigma models, which are distinct because their first integrals contain a different time dependent phase factor. We then show that with the gauge choice $k = \sqrt{\Lambda}/ tg (2 \sqrt{\Lambda}t)$ the same couple of first integrals indeed solves exactly the Einstein equations for every Riemann surface. The $X^A=X^A(x^mu)$ polydromic mapping which extends the standard immersion of a constant curvature three-dimensional surface in a flat four-dimensional space to the case of external point sources or topology, is calculable with a simple algebraic formula in terms only of the two sigma model solutions f and g. A trivial time translation of this formalism allows us to introduce a new method which is suitable to study the scattering of black holes in (2+1) AdS gravity.
No associations
LandOfFree
(2+1)-AdS Gravity on Riemann Surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with (2+1)-AdS Gravity on Riemann Surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and (2+1)-AdS Gravity on Riemann Surfaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-286333