Joins for (Augmented) Simplicial Sets

We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.Comment: 8 page

The damping of gravitational waves in dust

We examine a simple model of interaction of gravitational waves with matter (primarily represented by dust). The aim is to investigate a possible damping effect on the intensity of gravitational wave when passing through media. This might be important for gravitational wave astronomy when the sources are obscured by dust or molecular clouds.Comment: 7 pages, accepted to Phys. Sc

Moving frames for cotangent bundles

Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep. Math. Phy

Development of learning objectives for neurology in a veterinary curriculum: part I: undergraduates

Background With an increasing caseload of veterinary neurology patients in first opinion practice, there is a requirement to establish relevant learning objectives for veterinary neurology encompassing knowledge, skills and attitudes for veterinary undergraduate students in Europe. With help of experts in veterinary neurology from the European College of Veterinary Neurology (ECVN) and the European Society of Veterinary Neurology (ESVN) a survey of veterinary neurologic learning objectives using a modified Delphi method was conducted. The first phase comprised the development of a draft job description and learning objectives by a working group established by the ECVN. In the second phase, a quantitative questionnaire (multiple choice, Likert scale and free text) covering 140 learning objectives and subdivided into 8 categories was sent to 341 ESVN and ECVN members and a return rate of 62% (n = 213/341) was achieved. Results Of these 140 learning objectives ECVN Diplomates and ESVN members considered 42 (30%) objectives as not necessary for standard clinical veterinary neurology training, 94 (67%) were graded to be learned at a beginner level and 4 (3%) at an advanced level. The following objectives were interpreted as the most important day one skills: interpret laboratory tests, perform a neurological examination and establish a neuroanatomical localization. In this survey the three most important diseases of the central nervous system included epilepsy, intervertebral disc disease and inflammatory diseases. The three most important diseases of the peripheral nervous system included polyradiculoneuritis, myasthenia gravis and toxic neuropathies. Conclusions The results of this study should help to reform the veterinary curriculum regarding neurology and may reduce the phenomenon of “Neurophobia”.</p

Killing vectors and anisotropy

We consider an action that can generate fluids with three unequal stresses for metrics with a spacelike Killing vector. The parameters in the action are directly related to the stress anisotropies. The field equations following from the action are applied to an anisotropic cosmological expansion and an extension of the Gott-Hiscock cosmic string

Interpreting the C-metric

The basic properties of the C-metric are well known. It describes a pair of causally separated black holes which accelerate in opposite directions under the action of forces represented by conical singularities. However, these properties can be demonstrated much more transparently by making use of recently developed coordinate systems for which the metric functions have a simple factor structure. These enable us to obtain explicit Kruskal-Szekeres-type extensions through the horizons and construct two-dimensional conformal Penrose diagrams. We then combine these into a three-dimensional picture which illustrates the global causal structure of the space-time outside the black hole horizons. Using both the weak field limit and some invariant quantities, we give a direct physical interpretation of the parameters which appear in the new form of the metric. For completeness, relations to other familiar coordinate systems are also discussed.Comment: 22 pages, 14 figures (low-resolution figures; for the version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/ or http://www-staff.lboro.ac.uk/~majbg/

Isotropic Solutions of the Einstein-Liouville Equations

The gravitational field generated by a gas whose one-particle distribution function obeys the Liouville equation is examined under the following assumptions: First, the distribution is locally isotropic in momentum space with respect to some world-velocity field; second, if the particles have rest-mass zero, the gas is irrotational. It is shown that the model is then either stationary or a Robertson-Walker model. The time dependence of the radius in the Robertson-Walker models is given in terms of integrals containing the distribution function

Distance-redshift from an optical metric that includes absorption

We show that it is possible to equate the intensity reduction of a light wave caused by weak absorption with a geometrical reduction in intensity caused by a "transverse" conformal transformation of the spacetime metric in which the wave travels. We are consequently able to modify Gordon's optical metric to account for electromagnetic properties of ponderable material whose properties include both refraction and absorption. Unlike refraction alone however, including absorption requires a modification of the optical metric that depends on the eikonal of the wave itself. We derive the distance-redshift relation from the modified optical metric for Friedman-Lema\^itre-Robertson-Walker spacetimes whose cosmic fluid has associated refraction and absorption coefficients. We then fit the current supernovae data and provide an alternate explanation (other than dark energy) of the apparent acceleration of the universe.Comment: 2 figure

Schwarzschild horizon and the gravitational redshift formula

The gravitational redshift formula is usually derived in the geometric optics approximation. In this note we consider an exact formulation of the problem in the Schwarzschild space-time, with the intention to clarify under what conditions this redshift law is valid. It is shown that in the case of shocks the radial component of the Poynting vector can scale according to the redshift formula, under a suitable condition. If that condition is not satisfied, then the effect of the backscattering can lead to significant modifications. The obtained results imply that the energy flux of the short wavelength radiation obeys the standard gravitational redshift formula while the energy flux of long waves can scale differently, with redshifts being dependent on the frequency.Comment: Revtex, 5 p. Rewritten Sec. II, minor changes in Secs III - VII. To appear in the Classical and Quantum Gravit