Related papers: Some open questions on anti-de Sitter geometry
We study the relationship between Lorentz harmonic maps into the hyperbolic plane and spacelike surfaces in anti-de Sitter 3-space. Using loop group techniques, we develop a DPW-type representation for Lorentz harmonic maps and provide an…
Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space (other than the octonion hyperbolic plane), and consider the space L(M) of oriented geodesics of M. The space L(M) is…
Asymptotically locally AdS black hole geometries of dimension d > 2 are studied for nontrivial topologies of the transverse section. These geometries are static solutions of a set of theories labeled by an integer 0 < k < [(d-1)/2] which…
Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra…
We study anti-de Sitter black holes in 2+1 dimensions in terms of Chern Simons gauge theory of anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all…
We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with…
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…
We consider the geometry of anti-de-Sitter (AdS) black hole thermodynamics in four dimensions, where the equation of state in the extended phase space formalism allows explicit comparison with normal fluid systems. We show that for the…
In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…
It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The…
We study the principal curvatures of properly embedded constant mean curvature hypersurfaces in the Anti-de Sitter space $\mathbb{H}^{n,1}$. We generalize the notion of convex hull and give an upper bound on the principal curvatures which…
We consider a time-dependent $\mathcal{O}(1/G)$ deformation of pure de Sitter (dS) space in dS gravity coupled to a massless scalar field. It is the dS counterpart of the AdS Janus deformation and interpolates two asymptotically dS spaces…
We study proper, isometric actions of nonsolvable discrete groups Gamma on the 3-dimensional Minkowski space R^{2,1} as limits of actions on the 3-dimensional anti-de Sitter space AdS^3. To each such action is associated a deformation of a…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the…
We investigate the topological black holes in a special class of Lovelock gravity. In the odd dimensions, the action is the Chern-Simons form for the anti-de Sitter group. In the even dimensions, it is the Euler density constructed with the…
The generalized connections of the (anti)-de Sitter space symmetry algebra, which are differential forms of arbitrary degree with values in any irreducible (spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It is…
We consider minimal surfaces in three dimensional anti-de-Sitter space that end at the AdS boundary on a polygon given by a sequence of null segments. The problem can be reduced to a certain generalized Sinh-Gordon equation and to SU(2)…
We describe the space of isometric immersions from the Lorentz plane $L^2$ into the 3-dimensional anti-de Sitter space, and solve several open problems of this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from the…
We propose supergravity duals to non-trivial fixed points of the renormalization group in three dimensions with ADE global symmetries. All the fixed point symmetries are identified with space-time symmetries.