OPTIS - a satellite-based test of Special and General Relativity

A new satellite based test of Special and General Relativity is proposed. For the Michelson-Morley experiment we expect an improvement of at least three orders of magnitude, and for the Kennedy-Thorndike experiment an improvement of more than one order of magnitude. Furthermore, an improvement by two orders of the test of the universality of the gravitational red shift by comparison of an atomic clock with an optical clock is projected. The tests are based on ultrastable optical cavities, an atomic clock and a comb generator.Comment: To appear in Class. Quantum Gra

A model universe with variable dimension: Expansion as decrumpling

We propose a model universe, in which the dimension of the space is a continuous variable, which can take any real positive number. The dynamics leads to a model in which the universe has no singularity. The difference between our model and the standard Friedman-Robertson-Walker models become effective for times much before the presently accepted age of the universe.Comment: 12 pages, emTeX version 3.0, no figure

Product Integral Representations of Wilson Lines and Wilson Loops, and Non-Abelian Stokes Theorem

We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as approximating them with partial sums, their convergence, and their behavior under gauge transformations. We also obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes theorem.Comment: 20 pages, LaTe

Holographic Thermodynamic on the Brane in Topological Reissner-Nordstr\"om de Sitter Space

We consider the brane universe in the bulk background of the topological Reissner-Nordstr\"om de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy-Verlinde formula for the CFT with an charge and cosmological constant, for any values of the curvature parameter $k$ in the Friedmann equations.Comment: 8 page