Related papers: Hamiltonian structure and quantization of 2+1 dime…
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge is of hamiltonian nature. We give the exact diffeomorphism which transforms the expression of the spinning cone geometry in the Deser,…
A summary is given of some results and perspectives of the hamiltonian ADM approach to 2+1 dimensional gravity. After recalling the classical results for closed universes in absence of matter we go over the the case in which matter is…
We develop the formalism for canonical reduction of $(1+1)$--dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the…
After briefly reviewing the hamiltonian approach to 2+1 dimensional gravity in absence of matter on closed universes, we consider 2+1 dimensional gravity coupled to point particles in an open universe. We show that the hamiltonian structure…
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…
The 2+1+1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double…
A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a result is related to the uniformization of the the sphere punctured by n conical…
We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Non-linear terms are found up to…
We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but…
The Hamiltonian formulation of Horava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we…
We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the…
We show that 't Hooft's representation of (2+1)-dimensional gravity in terms of flat polygonal tiles is closely related to a gauge-fixed version of the covariant Hamiltonian lattice theory. 't Hooft's gauge is remarkable in that it leads to…
We develop a systematic Hamiltonian formulation for a gravitating topological matter system in three-dimensional spacetime, coupling a scalar gauge field and a rank-2 antisymmetric gauge field to Einstein--Cartan gravity. We perform the…
Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…