Weak distinction and the optimal definition of causal continuity

Causal continuity is usually defined by imposing the conditions (i) distinction and (ii) reflectivity. It is proved here that a new causality property which stays between weak distinction and causality, called feeble distinction, can actually replace distinction in the definition of causal continuity. An intermediate proof shows that feeble distinction and future (past) reflectivity implies past (resp. future) distinction. Some new characterizations of weak distinction and reflectivity are given.Comment: 9 pages, 2 figures. v2: improved and expanded version. v3: a few misprints have been corrected and a reference has been update

On the causal properties of warped product spacetimes

It is shown that the warped product spacetime P=M *_f H, where H is a complete Riemannian manifold, and the original spacetime M share necessarily the same causality properties, the only exceptions being the properties of causal continuity and causal simplicity which present some subtleties. For instance, it is shown that if diamH=+\infty, the direct product spacetime P=M*H is causally simple if and only if (M,g) is causally simple, the Lorentzian distance on M is continuous and any two causally related events at finite distance are connected by a maximizing geodesic. Similar conditions are found for the causal continuity property. Some new results concerning the behavior of the Lorentzian distance on distinguishing, causally continuous, and causally simple spacetimes are obtained. Finally, a formula which gives the Lorentzian distance on the direct product in terms of the distances on the two factors (M,g) and (H,h) is obtained.Comment: 22 pages, 2 figures, uses the package psfra

The causal ladder and the strength of K-causality. I

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The causal hierarchy of spacetime is built from chronology up to K-causality and new characterizations of the distinction and strong causality properties are obtained. The closure of the causal future is not transitive, as a consequence its repeated composition leads to an infinite causal subladder between strong causality and K-causality - the A-causality subladder. A spacetime example is given which proves that K-causality differs from infinite A-causality.Comment: 16 pages, one figure. Old title: ``On the relationship between K-causality and infinite A-causality''. Some typos fixed; small change in the proof of lemma 4.

A Note on Non-compact Cauchy surface

It is shown that if a space-time has non-compact Cauchy surface, then its topological, differentiable, and causal structure are completely determined by a class of compact subsets of its Cauchy surface. Since causal structure determines its topological, differentiable, and conformal structure of space-time, this gives a natural way to encode the corresponding structures into its Cauchy surface

The causal boundary of wave-type spacetimes

A complete and systematic approach to compute the causal boundary of wave-type spacetimes is carried out. The case of a 1-dimensional boundary is specially analyzed and its critical appearance in pp-wave type spacetimes is emphasized. In particular, the corresponding results obtained in the framework of the AdS/CFT correspondence for holography on the boundary, are reinterpreted and very widely generalized. Technically, a recent new definition of causal boundary is used and stressed. Moreover, a set of mathematical tools is introduced (analytical functional approach, Sturm-Liouville theory, Fermat-type arrival time, Busemann-type functions).Comment: 41 pages, 1 table. Included 4 new figures, and some small modifications. To appear in JHE

The Role of TiO2 Doping on RuO2-Coated Electrodes for the Water Oxidation Reaction

Electrochemical water splitting into H2 and O2 presents a significant and challenging energy loss due to the high overpotential required at the anode. Today, in industrially relevant applications, dimensionally stable anodes (DSA) based on the electrocatalytic active RuO2 are conventionally utilized. To enhance the resistance against corrosion, incorporation of TiO2 in the RuO2-coated electrodes is widely employed. In the present work we have used scanning electrochemical microscopy (SECM) to demonstrate that TiO2-doped RuO2-coated electrodes, in addition to being more durable, also show an electrocatalytic activity that is, on average, 13% higher as compared to the pure RuO2-coated electrodes. We also demonstrate that cracks in the pure RuO2 coating are the most active zones, probably because Ti from the Ti support has diffused into the first applied layer of the RuO2 coating. To reveal the nature of this enhanced activity for water oxidation displayed on TiO2-doped RuO2 electrodes, we have employed X-ray photoelectron spectroscopy (XPS) for material characterization. The results show that the electrocatalytic activity enhancement displayed on the mixed (Ru1–x:Tix)O2 coating is promoted through a charge transfer from the RuO2 to the TiO2, which provides new and more reactive sites designated as activated RuO2δ+.This study has partly been carried out in the framework of the European Commission FP7 Initial Training Network “ELCAT”, Grant Agreement No. 214936-2. Portions of this research were performed at SPring-8 with the approval of Japan Synchrotron Radiation Research Institute as Nanotechnology Support Project of the Ministry of Education, Culture, Sports, Science and Technology (Proposal No. 2007A2005 and 2008A1671/BL-47XU)

Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness

By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained, in terms of the convexity of the boundary of a domain in a Finsler n or (n+1)-space of Randers type. The latter convexity is analyzed in depth and, as a consequence, the causal simplicity and the existence of causal geodesics confined in the region and connecting a point to a stationary line are characterized. Applications to asymptotically flat spacetimes include the light-convexity of stationary hypersurfaces which project in a spacelike section of an end onto a sphere of large radius, as well as the characterization of their time-convexity with natural physical interpretations. The lens effect of both light rays and freely falling massive particles with a finite lifetime, (i.e. the multiplicity of such connecting curves) is characterized in terms of the focalization of the geodesics in the underlying Randers manifolds.Comment: AMSLaTex, 41 pages. v2 is a major revision: new discussions on physical applicability of the results, especially to asymptotically flat spacetimes; references adde