In this paper we assume the de Sitter space version of black hole Complementarity which states that a single causal patch of de Sitter space is described as an isolated finite temperature cavity bounded by a horizon which allows no loss of information. We discuss the how the symmetries of de Sitter space should be implemented. Then we prove a no go theorem for implementing the symmetries if the...

We consider the contribution to the entropy from fields in the background of a curved time-independent metric. To account for the curvature of space, we postulate a position-dependent UV cutoff. We argue that a UV cutoff on energy naturally implies an IR cutoff on distance. With this procedure, we calculate the scalar contribution in a background anti-de Sitter space, the exterior of a black ho...

We consider 2 + 1 dimensional gravity with a cosmological constant, and explore a duality that exists between space-times that have the De Sitter group SO(3, 1) as its local isometry group. In particular, the Lorentzian theory with a positive cosmological constant is dual to the Euclidean theory with a negative cosmological constant. We use this duality to construct a mapping between apparently...

Two new quantum anti-de Sitter so(4, 2) and de Sitter so(5, 1) algebras are presented. These deformations are called either ‘time-type’ or ‘space-type’ according to the dimensional properties of the deformation parameter. Their Hopf structure, universal R matrix and differential-difference realization are obtained in a unified setting by considering a contraction parameter related to the speed ...

We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an “elliptic” identification provides a concrete realization of observer complementarity in de Sitter space: every observer has complete information. This proposal naturally leads to a holographic description in which the dual (conformal) field theory lives on a single sphere. Correlation fu...

We study vacuum and thermal expectation values of quantum scalar and fermion fields on anti-de Sitter space-time. Anti-de Sitter space-time is maximally symmetric and this enables expressions for the scalar and fermion vacuum Feynman Green’s functions to be derived in closed form. We employ Hadamard renormalization to find the vacuum expectation values. The thermal Feynman Green’s functions are...

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 Lorentz part of the anti-de Sitter curvature tensor. The Lovelock coefficients are reduced to two independent parameters: cosmological constant and gravitat...

We study the thermodynamic stability of charged black holes in gauged supergravity theories in D = 5, D = 4 and D = 7. We find explicitly the location of the Hawking-Page phase transition between charged black holes and the pure anti-de Sitter space-time, both in the grand-canonical ensemble, where electric potentials are held fixed, and in the canonical ensemble, where total charges are held f...

We describe a class of impulsive gravitational waves which propagate either in a de Sitter or an anti-de Sitter background. They are conformal to impulsive waves of Kundt’s class. In a background with positive cosmological constant they are spherical (but non-expanding) waves generated by pairs of particles with arbitrary multipole structure propagating in opposite directions. When the cosmolog...

The solutions of the Bogomolny equation in 2+1 dimensional anti-de Sitter space-time are obtained by using Darboux transformations with both constant spectral parameters and variable “spectral parameters”. These solutions give the Yang-Mills-Higgs fields in 2+1 dimensional antide Sitter space-time. Some examples in SU(2) case are considered and qualitative asymptotic behaviors of the solutions ...