Given a compact n-manifold Σ with a flat conformal structure, there is a canonical procedure for constructing an associated (n + 1)-dimensional de Sitter spacetime homeomorphic to Σ× (0,∞); we call these standard de Sitter spacetimes. Our main theorem is a classification of compact de Sitter manifolds; it asserts that every de Sitter spacetime which is a small regular neighborhood of a closed s...

We propose that the state represented by the Nariai black hole inside de Sitter space is the ground state of the de Sitter gravity, while the pure de Sitter space is the maximal energy state. With this point of view, we investigate thermodynamics of de Sitter space, we find that if there is a dual field theory, this theory can not be a CFT in a fixed dimension. Near the Nariai limit, we conject...

It is well known that the semi-Riemannian (pseudo-Riemannian) manifolds (M,g) of Lorentzian signature play a special role in geometry and physics, and that they are models of space time of general relativity. Let Mn+1 p (c) be an (n+1)-dimensional complete connected semi-Riemannian manifold with constant sectional curvature c and index p (see [13, page 227]). It is called an indefinite space fo...

We consider a brane-world construction which incorporates a finite region of flat space, “the box,” surrounded by a region of anti-de Sitter space. This hybrid construction provides a framework which interpolates between the scenario proposed by Arkani-Hamed, Dimopoulos and Dvali, and that proposed by Randall and Sundrum. Within this composite framework, we investigate the effects of resonant m...

We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, p...

The local and global thermal phase structure for asymptotically anti-de Sitter black holes charged under an abelian gauge group, with both Gauss-Bonnet and quartic field strength corrections, is mapped out for all parameter space. We work in the grand canonical ensemble where the external electric potential is held fixed. The analysis is performed in an arbitrary number of dimensions, for all t...

The graviton propagator in a de Sitter background is found to be divergent. We show that as a consequence of this divergence, de Sitter space is not a solution of the equations of motion of the complete theory. If we start from de Sitter space-as a classical ground state, quantum corrections change it into flat Minkowski.

We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The perturbation analysis around the cosmological horizon of Kerr-de Sitter space reveals a mixing between the dilaton and other fields. Introducing a gauge (dilaton gauge), we can disentangle this mixing completely and obtain ...

A special relativity based on the de Sitter group is introduced. Like ordinary special relativity, it retains the quotient character of spacetime, and consequently a notion of homogeneity. This means that the underlying spacetime will be a de Sitter spacetime, the quotient space between de Sitter and the Lorentz groups. Since the local symmetry will also be given by the de Sitter group, each ta...