Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Rotational Surfaces in L3\mathbb{L}^3 and Solutions in the Nonlinear Sigma Model

The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. The main tools are the equivalence of the two-dimensional O(2,1) Nonlinear Sigma Model and the Willmore problem, and the description of the surfaces with rotational symmetry. A complete classification of such surfaces is obtained in this paper. Indeed, a huge new family of Lorentzian rotational surfaces with a space-like axis is presented. The description of this new class of surfaces is based on a technique of surgery and a gluing process, which is illustrated by an algorithm.Comment: PACS: 11.10.Lm; 11.10.Ef; 11.15.-q; 11.30.-j; 02.30.-f; 02.40.-k. 45 pages, 11 figure

Gravitational collapse of spherically symmetric stars in noncommutative general relativity

Gravitational collapse of a class of spherically symmetric stars is investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to oncommutative spacetimes with gravitational collapse

An improved measurement of electron-ion recombination in high-pressure xenon gas

We report on results obtained with the NEXT-DEMO prototype of the NEXT-100 high-pressure xenon gas time projection chamber (TPC), exposed to an alpha decay calibration source. Compared to our previous measurements with alpha particles, an upgraded detector and improved analysis techniques have been used. We measure event-by-event correlated fluctuations between ionization and scintillation due to electron-ion recombination in the gas, with correlation coeffcients between -0.80 and -0.56 depending on the drift field conditions. By combining the two signals, we obtain a 2.8% FWHM energy resolution for 5.49 MeV alpha particles and a measurement of the optical gain of the electroluminescent TPC. The improved energy resolution also allows us to measure the specific activity of the radon in the gas due to natural impurities. Finally, we measure the average ratio of excited to ionized atoms produced in the xenon gas by alpha particles to be 0:561 0:045, translating into an average energy to produce a primary scintillation photon ofWex = (39:2 3:2) eV.This work was supported by the following agencies and institutions: the European Research Council under the Advanced Grant 339787-NEXT; the Ministerio de Economia y Competitividad of Spain under grants CONSOLIDER-Ingenio 2010 CSD2008-0037 (CUP), FPA2009-13697-C04 and FIS2012-37947-C04; the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231; and the Portuguese FCT and FEDER through the program COMPETE, project PTDC/FIS/103860/2008.Serra, L.; Sorel, M.; Alvarez, V.; Borges, FIG.; Camargo, M.; Carcel, S.; Cebrian, S.... (2015). An improved measurement of electron-ion recombination in high-pressure xenon gas. Journal of Instrumentation. 10:1-19. https://doi.org/10.1088/1748-0221/10/03/P03025S1191

Near-intrinsic energy resolution for 30-662 keV gamma rays in a high pressure xenon electroluminescent TPC

We present the design, data and results from the NEXT prototype for Double Beta and Dark Matter (NEXT-DBDM) detector, a high-pressure gaseous natural xenon electroluminescent time projection chamber (TPC) that was built at the Lawrence Berkeley National Laboratory. It is a prototype of the planned NEXT-100 136Xe neutrino-less double beta decay (0νββ) experiment with the main objectives of demonstrating near-intrinsic energy resolution at energies up to 662 keV and of optimizing the NEXT-100 detector design and operating parameters. Energy resolutions of ∼1% FWHM for 662 keV gamma rays were obtained at 10 and 15 atm and ∼5% FWHM for 30 keV fluorescence xenon X-rays. These results demonstrate that 0.5% FWHM resolutions for the 2,459 keV hypothetical neutrino-less double beta decay peak are realizable. This energy resolution is a factor 7 to 20 better than that of the current leading 0νββ experiments using liquid xenon and thus represents a significant advancement. We present also first results from a track imaging system consisting of 64 silicon photo-multipliers recently installed in NEXT-DBDM that, along with the excellent energy resolution, demonstrates the key functionalities required for the NEXT-100 0νββ search

Ionization and scintillation of nuclear recoils in gaseous xenon

Abstract Ionization and scintillation produced by nuclear recoils in gaseous xenon at approximately 14 bar have been simultaneously observed in an electroluminescent time projection chamber. Neutrons from radioisotope α-Be neutron sources were used to induce xenon nuclear recoils, and the observed recoil spectra were compared to a detailed Monte Carlo employing estimated ionization and scintillation yields for nuclear recoils. The ability to discriminate between electronic and nuclear recoils using the ratio of ionization to primary scintillation is demonstrated. These results encourage further investigation on the use of xenon in the gas phase as a detector medium in dark matter direct detection experiments.This work was supported by the following agencies and institutions: the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy, and the National Energy Research Scientific Computing Center (NERSC), supported by the Office of Science of the U.S. Department of Energy, both under Contract no. DE-AC02-05CH11231; the European Research Council under the Advanced Grant 339787-NEXT; the Ministerio de Economia y Competitividad of Spain under Grants CONSOLIDER-Ingenio 2010 C5D2008-0037 (CUP), FPA2009-13697-004-04, FPA2009-13697-C04-01, FIS2012-37947-C04-01, FIS2012-37947-C04-02, FIS2012-37947-C04-03, and FIS2012-37947-C04-04; and the Portuguese FCT and FEDER through the program COMPETE, Projects PTDC/FIS/103860/2008 and PTDC/FIS/112272/2009. J. Renner acknowledges the support of a Department of Energy National Nuclear Security Administration Stewardship Science Graduate Fellowship, grant number DE-FC52-08NA28752.Renner, J.; Gehman, VM.; Goldschmidt, A.; Matis, HS.; Miller, T.; Nakajima, Y.; Nygren, D.... (2015). Ionization and scintillation of nuclear recoils in gaseous xenon. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 793:62-74. https://doi.org/10.1016/j.nima.2015.04.057S627479