On the definition and examples of cones and finsler spacetimes

The authors warmly acknowledge Professor Daniel Azagra (Universidad Complutense, Madrid) his advise on approximation of convex functions as well as Profs. Kostelecky (Indiana University), Fuster (University of Technology, Eindhoven), Stavrinos (University of Athens), Pfeifer (University of Tartu), Perlick (University of Bremen) and Makhmali (Institute of Mathematics, Warsaw) their comments on a preliminary version of the article. The careful revision by the referee is also acknowledged. This work is a result of the activity developed within the framework of the Programme in Support of Excellence Groups of the Region de Murcia, Spain, by Fundacion Seneca, Science and Technology Agency of the Region de Murcia. MAJ was partially supported by MINECO/FEDER project reference MTM2015-65430-P and Fundacion Seneca project reference 19901/GERM/15, Spain and MS by Spanish MINECO/ERDF project reference MTM2016-78807-C2-1-P.A systematic study of (smooth, strong) cone structures C and Lorentz–Finsler metrics L is carried out. As a link between both notions, cone triples (Ω,T,F), where Ω (resp. T) is a 1-form (resp. vector field) with Ω(T)≡1 and F, a Finsler metric on ker(Ω), are introduced. Explicit descriptions of all the Finsler spacetimes are given, paying special attention to stationary and static ones, as well as to issues related to differentiability. In particular, cone structures C are bijectively associated with classes of anisotropically conformal metrics L, and the notion of cone geodesic is introduced consistently with both structures. As a non-relativistic application, the time-dependent Zermelo navigation problem is posed rigorously, and its general solution is provided.MINECO/FEDER project, Spain MTM2015-65430-PFundacion Seneca 19901/GERM/15Spanish MINECO/ERDF project MTM2016-78807-C2-1-

Anapole nanolasers for mode-locking and ultrafast pulse generation

Nanophotonics is a rapidly developing field of research with many suggestions for a design of nanoantennas, sensors and miniature metadevices. Despite many proposals for passive nanophotonic devices, the efficient coupling of light to nanoscale optical structures remains a major challenge. In this article, we propose a nanoscale laser based on a tightly confined anapole mode. By harnessing the non-radiating nature of the anapole state, we show how to engineer nanolasers based on InGaAs nanodisks as on-chip sources with unique optical properties. Leveraging on the near-field character of anapole modes, we demonstrate a spontaneously polarized nanolaser able to couple light into waveguide channels with four orders of magnitude intensity than classical nanolasers, as well as the generation of ultrafast (of 100 fs) pulses via spontaneous mode locking of several anapoles. Anapole nanolasers offer an attractive platform for monolithically integrated, silicon photonics sources for advanced and efficient nanoscale circuitry

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