Related papers: Girard Type Theorems for de Sitter Triangles with …

We characterize isotropic trialitarian triples in terms of the Schur indices of the underlying algebras over a base field $F$ of arbitrary characteristic satisfying $I_q^3 F=0$. We also construct anisotropic trialitarian triples over such…

It is shown that, when f'' is non-vanishing, metric f(R) gravity is completely equivalent to a scalar-tensor theory (with zero Brans-Dicke parameter) with respect to perturbations of de Sitter space, contrary to previous expectations.…

This paper deals with some two-parameter solutions to the spherically symmetric, vacuum Einstein equations which, we argue, are more general than de Sitter solution. The global structure of one such spacetimes and its extension to the…

We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic $3$-space and in de Sitter space. Several dualities of invariants are pointed out.

We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not…

From the group theoretical point of view, it is proved that the theory of linear conformal gravity should be written in terms of a tensor field of rank-3 and mixed symmetry [Binegar, et al, Phys. Rev. D 27, (1983) 2249]. We obtained such a…

I argue against the widespread notion that manifest de Sitter invariance on the full de Sitter manifold is either useful or even attainable in gauge theories. Green's functions and propagators computed in a de Sitter invariant gauge are…

It is known that de Sitter spacetime can be seen as the solution of field equation for completely isotropic matter. In the present paper a new class of exact solutions in spherical symmetry is found and discussed, such that the…

The quantization of circular strings in an anti-de Sitter background spacetime is performed, obtaining a discrete spectrum for the string mass. A comparison with a four-dimensional homogeneous and isotropic spacetime coupled to a conformal…

We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find…

This paper discusses a theory of natural circular dichroism in the x-ray region. Integrated spectra are interpreted in terms of microscopic effective operators, which are derived in the framework of a localised (atomic) model. It is shown…

We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting…

We analyze the behavior of causal geodesics on a Kerr-de Sitter spacetime with particular emphasis on their completeness property. We set up an initial value problem (IVP) whose solutions lead to a global understanding of causal geodesics…

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 consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain ``stringy regions'' that from a classical point of view…

We introduce null surfaces (or nullcone fronts) of pseudo-spherical spacelike framed curves in the three-dimensional anti-de Sitter space. These surfaces are formed by the light rays emitted from points on anti-de Sitter spacelike framed…

We evaluate an analogue of an integral of Dirichlet over the sphere S^D, but with an integrand that is independent of [(D + 1)/2] Killing coordinates. As an application, we evaluate an integral that arises when comparing a conformal fluid…

We quantize a massive scalar field in de Sitter spacetime and derive the S-matrix for the general interacting theory. Using the general boundary formulation of quantum field theory, we also propose a new type of S-matrix derived from the…

From the viewpoint of the division by zero $(0/0=1/0=z/0=0)$ and the division by zero calculus, we will show that in the very beautiful theorem by Descartes on three touching circles is valid for lines and points for circles except for one…

Let $\Sigma$ be a bounded surface. We prove the Dehn-Nielsen-Baer theorem for bounded surfaces to show that the mapping class group of $\Sigma$ is isomorphic to the automorphisms of the fundamental groupoid of $\Sigma$ that fix loops around…