A set of data supposed to give possible axioms for spacetimes. It is hoped that such a proposal can serve to become a testing ground on the way to a general formulation. At the moment, the axioms are known to be sufficient for cases with a sufficient number of symmetries, in particular for 1+1 de Sitter spacetime. A major shortcoming of applications of noncommutative geometry to high energy phy...

Recently it has been suggested that non-gaussian inflationary perturbations can be usefully analysed in terms of a putative dual gauge theory defined on the future conformal infinity generated by an accelerating cosmology. The problem is that unitarity of this gauge theory implies a strong constraint [the “Strominger bound”] on the matter fields in the bulk. We argue that the bound is just a re...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology. 1 Branching MWI space-times Two basic types of branching universe have been suggested in modern mathematical physics: universes which branch in a style befitting the ‘many-worlds...

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E 1 are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrin...

Scalar field theories with appropriate potentials in Minkowski space can have timedependent classical solutions containing topological defects which correspond to S-branes i.e. branes all of whose tangential dimensions are spacelike. It is argued that such Sbranes arise in string theory as time-dependent solutions of the worldvolume tachyon field of an unstable D-brane or D-brane-anti-D-brane p...

In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from no incoming radiation condition $\mathcal I^-$ and polynomially decaying data, $r\phi_\ell\sim t^{-1}$ as $t\to-\infty$, either timelike boundary of constant area radius (I) or an ingoing null hypersurface (I...

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector fiel...