Topics in 2 + 1 gravity and conformal field theory
Johnson, Richard Gunn (2009) Topics in 2 + 1 gravity and conformal field theory. PhD thesis, University of Nottingham.
We study the Hamiltonian dynamics for a system of two colliding point particles coupled to (2+1)-dimensional gravity with a negative cosmological constant by anchoring the dynamics of the system to its spatial infinity. We reduce the Chern-Simons formulation of the gravitational action, finding the reduced Hamiltonian for three special cases of the particle masses, in a phase space chart coordinatised by the geodesic distance between the two particles and its conjugate momentum. The dimension of the reduced phase space is two. At the threshold of black hole formation, the black hole mass depends linearly on the momentum, in agreement with previous analysis in a holonomy-based phase space chart. We use the reduced action to compute the semiclassical probability amplitude of two particles to tunnel out of the black hole, finding that the imaginary part of the action is equal to the Bekenstein-Hawking entropy of the hole.
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