Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$ time. This result is related to Yau's Lorentzian splitting conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review

Yields of oxidized volatile organic compounds during the OH radical initiated oxidation of isoprene, methyl vinyl ketone, and methacrolein under high-NO_x conditions

We present first-generation and total production yields of glyoxal, methylglyoxal, glycolaldehyde, and hydroxyacetone from the oxidation of isoprene, methyl vinyl ketone (MVK), and methacrolein (MACR) with OH under high NO_x conditions. Several of these first-generation yields are not included in commonly used chemical mechanisms, such as the Leeds Master Chemical Mechanism (MCM) v. 3.2. The first-generation yield of glyoxal from isoprene was determined to be 2.1 (±0.6)%. Inclusion of first-generation production of glyoxal, glycolaldehyde and hydroxyacetone from isoprene greatly improves performance of an MCM based model during the initial part of the experiments. In order to further improve performance of the MCM based model, higher generation glyoxal production was reduced by lowering the first-generation yield of glyoxal from C5 hydroxycarbonyls. The results suggest that glyoxal production from reaction of OH with isoprene under high NO_x conditions can be approximated by inclusion of a first-generation production term together with secondary production only via glycolaldehyde. Analogously, methylglyoxal production can be approximated by a first-generation production term from isoprene, and secondary production via MVK, MACR and hydroxyacetone. The first-generation yields reported here correspond to less than 5% of the total oxidized yield from isoprene and thus only have a small effect on the fate of isoprene. However, due to the abundance of isoprene, the combination of first-generation yields and reduced higher generation production of glyoxal from C5 hydroxycarbonyls is important for models that include the production of the small organic molecules from isoprene

Analysis of photochemical and dark glyoxal uptake: Implications for SOA formation

The dependence of glyoxal uptake onto deliquesced ammonium sulfate seed aerosol was studied under photochemical (light + hydroxyl radical (OH)) and dark conditions. In this study, the chemical composition of aerosol formed from glyoxal is identical in the presence or absence of OH. In addition, there was no observed OH dependence on either glyoxal uptake or glyoxal-driven aerosol growth for this study. These findings demonstrate that, for the system used here, glyoxal uptake is not affected by the presence of OH. In combination with previous studies, this shows that the exact nature of the type of seed aerosol, in particular the presence of a coating, has a large influence on fast photochemical uptake of glyoxal. Due to the challenge of relating this seed aerosol dependence to ambient conditions, this work highlights the resulting difficulty in quantitatively including SOA formation from glyoxal in models

Glyoxal uptake on ammonium sulphate seed aerosol: reaction products and reversibility of uptake under dark and irradiated conditions

Chamber studies of glyoxal uptake onto ammonium sulphate aerosol were performed under dark and irradiated conditions to gain further insight into processes controlling glyoxal uptake onto ambient aerosol. Organic fragments from glyoxal dimers and trimers were observed within the aerosol under dark and irradiated conditions. Glyoxal monomers and oligomers were the dominant organic compounds formed under the conditions of this study; glyoxal oligomer formation and overall organic growth were found to be reversible under dark conditions. Analysis of high-resolution time-of-flight aerosol mass spectra provides evidence for irreversible formation of carbon-nitrogen (C-N) compounds in the aerosol. We have identified 1H-imidazole-2-carboxaldehyde as one C-N product. To the authors' knowledge, this is the first time C-N compounds resulting from condensed phase reactions with ammonium sulphate seed have been detected in aerosol. Organosulphates were not detected under dark conditions. However, active photochemistry was found to occur within aerosol during irradiated experiments. Carboxylic acids and organic esters were identified within the aerosol. An organosulphate, which had been previously assigned as glyoxal sulphate in ambient samples and chamber studies of isoprene oxidation, was observed only in the irradiated experiments. Comparison with a laboratory synthesized standard and chemical considerations strongly suggest that this organosulphate is glycolic acid sulphate, an isomer of the previously proposed glyoxal sulphate. Our study shows that reversibility of glyoxal uptake should be taken into account in SOA models and also demonstrates the need for further investigation of C-N compound formation and photochemical processes, in particular organosulphate formation

Summary of the recent short-haul systems studies

The results of several NASA sponsored high density short haul air transportation systems studies are reported as well as analyzed. Included are the total STOL systems analysis approach, a companion STOL composites study conducted in conjunction with STOL systems studies, a STOL economic assessment study, an evaluation of STOL aircraft with and without externally blown flaps, an alternative STOL systems for the San Francisco Bay Area, and the quiet, clean experimental engine studies. Assumptions and results of these studies are summarized, their differences, analyzed, and the results compared with those in-house analyses performed by the Systems Studies Division of the NASA-Ames Research Center. Pertinent conclusions are developed and the more significant technology needs for the evaluation of a viable short haul transportation system are identified

Photooxidation of 2-methyl-3-buten-2-ol (MBO) as a potential source of secondary organic aerosol

2-Methyl-3-buten-2-ol (MBO) is an important biogenic hydrocarbon emitted in large quantities by pine forests. Atmospheric photooxidation of MBO is known to lead to oxygenated compounds, such as glycolaldehyde, which is the precursor to glyoxal. Recent studies have shown that the reactive uptake of glyoxal onto aqueous particles can lead to formation of secondary organic aerosol (SOA). In this work, MBO photooxidation under high- and low-NO_x conditions was performed in dual laboratory chambers to quantify the yield of glyoxal and investigate the potential for SOA formation. The yields of glycolaldehyde and 2-hydroxy-2-methylpropanal (HMPR), fragmentation products of MBO photooxidation, were observed to be lower at lower NO_x concentrations. Overall, the glyoxal yield from MBO photooxidation was 25% under high-NO_x and 4% under low-NO_x conditions. In the presence of wet ammonium sulfate seed and under high-NO_x conditions, glyoxal uptake and SOA formation were not observed conclusively, due to relatively low (<30 ppb) glyoxal concentrations. Slight aerosol formation was observed under low-NO_x and dry conditions, with aerosol mass yields on the order of 0.1%. The small amount of SOA was not related to glyoxal uptake, but is likely a result of reactions similar to those that generate isoprene SOA under low-NO_x conditions. The difference in aerosol yields between MBO and isoprene photooxidation under low-NO_x conditions is consistent with the difference in vapor pressures between triols (from MBO) and tetrols (from isoprene). Despite its structural similarity to isoprene, photooxidation of MBO is not expected to make a significant contribution to SOA formation

What is the topology of a Schwarzschild black hole?

We investigate the topology of Schwarzschild's black hole through the immersion of this space-time in spaces of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschild's black hole.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1102.446

The region with trapped surfaces in spherical symmetry, its core, and their boundaries

We consider the region $\mathscr{T}$ in spacetime containing future-trapped closed surfaces and its boundary \B, and derive some of their general properties. We then concentrate on the case of spherical symmetry, but the methods we use are general and applicable to other situations. We argue that closed trapped surfaces have a non-local property, "clairvoyance", which is inherited by \B. We prove that \B is not a marginally trapped tube in general, and that it can have portions in regions whose whole past is flat. For asymptotically flat black holes, we identify a general past barrier, well inside the event horizon, to the location of \B under physically reasonable conditions. We also define the core $\mathscr{Z}$ of the trapped region as that part of $\mathscr{T}$ which is indispensable to sustain closed trapped surfaces. We prove that the unique spherically symmetric dynamical horizon is the boundary of such a core, and we argue that this may serve to single it out. To illustrate the results, some explicit examples are discussed, namely Robertson-Walker geometries and the imploding Vaidya spacetime.Comment: 70 pages, 14 figures. Figure 6 has been replaced, and corrected. Minor changes around Propositions 10.3 and 10.4, and some typos correcte