Three-dimensional De Sitter Spacetime Research Articles

Conformal wave expansions for flat space amplitudes

The extended BMS algebra contains a conformal subgroup that acts on the celestial sphere as SO(1, 3). It is of interest to perform mode expansions of free fields in Minkowski spacetime that realize this symmetry in a simple way. In the present work we perform such a mode expansion for massive scalar fields using the unitary principal series representations of SO(1, 3) with a view to developing a holographic approach to gravity in asymptotically flat spacetime. These mode expansions are also of use in studying holography in three-dimensional de Sitter spacetime.

Singularities of worldsheets in spherical space–times

In this paper, the singularities of the geometry for four classes of worldsheets, which are respectively, located in three-dimensional hyperbolic space and three-dimensional de Sitter space–time are considered. Under the theoretical frame of geometry of space–time and as applications of singularity theory, it is shown that these worldsheets have two classes of singularities, that is, in the local sense, these four classes of worldsheets are, respectively, diffeomorphic to the cuspidal edge and the swallowtail. The first hyperbolic worldsheet and the second hyperbolic worldsheet are [Formula: see text]-dual to the tangent curves of spacelike curves. Moreover, it is also revealed that there is a close relationship between the types of singularities of worldsheets and a geometric invariant [Formula: see text], depending on whether [Formula: see text] or [Formula: see text] and [Formula: see text], the singularities of these worldsheets can be characterized by the geometric invariant. We provide two explicit examples of worldsheets to illustrate the theoretical results.

UPPER AND LOWER BOUNDS FOR THE VOLUME OF A COMPACT SPACELIKE HYPERSURFACE IN A GENERALIZED ROBERTSON–WALKER SPACETIME

We provide upper and lower bounds for the volume of a compact spacelike hypersurface in an (n + 1)-dimensional Generalized Robertson–Walker (GRW) spacetime in terms of the volume of the fiber, the hyperbolic angle function and the warping function. Under several geometrical and physical assumptions, we characterize the spacelike slices as the only spacelike hypersurfaces where these bounds are attained. As a consequence of these results, we get an upper bound for the first eigenvalue of a compact spacelike surface in a three-dimensional GRW spacetime whose fiber is a topological sphere, which includes the case of the three-dimensional De Sitter spacetime, and show that the bound is attained if and only if M is a spacelike slice.

Smeared hair and black holes in three-dimensional de Sitter spacetime

It is known that there is no three-dimensional analog of de Sitter black holes. I show that the analog does exist when non-Gaussian (i.e., ring-type) smearings of point matter hairs are considered. This provides a new way of constructing black hole solutions from hairs. I find that the obtained black hole solutions are quite different from the usual large black holes in that there are (i) large to small black hole transitions which may be considered as inverse Hawking-Page transitions and (ii) solitonlike (i.e., nonperturbative) behaviors. For Gaussian smearing, there is no black hole but a gravastar solution exists.

Quantum Mechanics of the Supplementary Series

Unitary, irreducible representations of the proper, orthochronous Lorentz group comprise the main series and the supplementary series. The main series is spanned by the complete set of eigenstates of the self-adjoint Casimir operator C1=−(1/2)M μν M μν , where M μν are generators of Lorentz transformations. The supplementary series has no such interpretation; moreover it is spurious from the point of view of functional analysis as it does not enter into the integral representation of an arbitrary test function. The author describes the physical context within which the supplementary series arises, nevertheless, in a natural way: it arises if we exponentiate a massless scalar quantum field living in three-dimensional de Sitter space-time and if the appropriate coupling constant is small enough.

Integrable Yang–Mills–Higgs equations in three-dimensional de Sitter space–time

This paper describes an integrable Yang–Mills–Higgs system on (2+1)-dimensional de Sitter space–time. It is the curved-space–time analog of the Bogomolnyi equations for monopoles on R3. A number of solutions, of various types, are constructed.