Related papers: 2+1 gravity, chaos and time machines
The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular…
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite…
For spacetimes with the topology $\IR\!\times\!T^2$, the action of (2+1)-dimensional gravity with negative cosmological constant $\La$ is written uniquely in terms of the time-independent traces of holonomies around two intersecting…
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and simply connected compact Lie groups and…
We find group cochains valued in currents giving explicit representatives for the $\text{GL}_2$-equivariant polylogarithm class of a torus. Based on the construction of weight-$2$ Eisenstein series for $\text{GL}_2$ from this polylogarithm…
Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the…
We develop a new perspective on the discretization of the phase space structure of gravity in 2+1 dimensions as a piecewise-flat geometry in 2 spatial dimensions. Starting from a subdivision of the continuum geometric and phase space…
We intend to study a new class of cosmological models in $f(R, T)$ modified theories of gravity, hence define the cosmological constant $\Lambda$ as a function of the trace of the stress energy-momentum-tensor $T$ and the Ricci scalar $R$,…
It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravitational path integral.…
The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a…
We introduce the (2+1)-spacetimes with compact space of genus g and with r gravitating particles which arise by ``Minkowskian suspensions of flat or hyperbolic cone surfaces'', by ``distinguished deformations'' of hyperbolic suspensions and…
We consider a topological field theory derived from the Chern - Simons action in (2+1) dimensions with the I(ISO(2,1)) group,and we investigate in detail the canonical structure of this theory.Originally developed as a topological theory of…
A physical interpretation of the recently discovered vast class of vacuum space-times, which stably violate the strong cosmic censor conjecture (in its usual broad formulation) in four dimensions, is exhibited. Namely, by elementary Morse…
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 examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…
Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the…
The extended conformal algebra (so)(2,3) of global, quantum, constants of motion in 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant is reviewed. It is shown that the 10 global constants form a complete set…
We define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to the Hausdorff dimension for metric spaces - that…
We extend the argument that spacetimes generated by two timelike particles in D=3 gravity (or equivalently by parallel-moving cosmic strings in D=4) permit closed timelike curves (CTC) only at the price of Misner identifications that…
We investigate the space ${\cal M}$ of classical solutions to Witten's formulation of 2+1 gravity on the manifold ${\bf R} \times T^2$. ${\cal M}$ is connected, unlike the spaces of classical solutions in the cases where $T^2$ is replaced…