We study aspects of the propagation of strings on BTZ black holes. After performing a careful analysis of the global spacetime structure of generic BTZ black holes, and its relation to the geometry of the SL(2, R) group manifold, we focus on the simplest case of the massless BTZ black hole. We study the SL(2, R) Wess-Zumino-Witten model in the worldsheet minisuperspace limit, taking into accoun...

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n− 2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by ...

Let X be a smooth manifold of dimension 1 + n endowed with a Lorentzian metric g. The energy tensor of a 2-form F is locally defined as Tab := − ( Fa Fbi − 1 4 F Fijgab ) . In this paper we characterize this tensor as the only 2-covariant natural tensor associated to a Lorentzian metric and a 2-form that is independent of the unit of scale and satisfies certain condition on its divergence. This...

I introduce a closeness function between causal Lorentzian geometries of finite volume and arbitrary underlying topology. The construction uses the fact that some information on the manifolds and metrics is encoded in the partial order that the causal structure of each metric induces among points randomly scattered in the corresponding manifold with uniform, finite density according to the volu...

We introduce a covariant formulation of Barbero-Immirzi connections, which are used in Loop Quantum Gravity to describe gravity. show that connections can be uniquely defined out given spin connection for any $(n+1)$-dimensional lorentzian manifold is spin. A remarkable result the presence real parameter feature unique $4$-dimensional case.

Abstract We consider an inverse boundary value problem for a semilinear wave equation on time-dependent Lorentzian manifold with time-like boundary. The coefficients of the nonlinear terms can be recovered in interior from knowledge Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams used to derive uniqueness.

Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more att...

We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dir...

We construct interpolation operators for functions taking values in a symmetric space—a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized as a homogeneous space whose cosets have canonical representatives by virtue of the generalized polar decomposition—a generalization of the well-known factorizat...