Geodesic Geometry of Black Holes

The study of geodesics is of intrinsic significance in the study of the geometry of space-time. In this thesis null, space-like and time-like geodesics are studied in the case of the space-times of Schwarzschild, Reissner-Nordstrouml;m and Kerr black holes. These space-times have been investigated with varying degrees of thoroughness in many articles and some books. However, there are some significant gaps in these treatments and the central aim of this thesis is to fill these gaps where necessary. Moreover, the following topics are covered for the first time. 1. In Chapter 4 a thorough treatment of the space-like geodesics of the Schwarzschild solutions has been given. These geodesics are the trajectories of Tachyons (faster than light particles) and are treated in a complete manner. This has been done by obtaining exact solutions and solving them numerically. 2. In Part II all solutions for geodesics for a Reissner-Nordstrouml;m black hole have been given in complete detail, i.e. time-like, null and space-like geodesics and orbit of a charged particle. 3. In Chapter 14 all solutions for geodesics in the equatorial plane of a Kerr black hole have been given in complete detail, i.e. time-like, null and space-like geodesics. 4. The study of special types of non-equatorial geodesics for a Kerr black hole have been given in complete detail, i.e. time-like (Chapter 17), null (Chapter 15) and space-like (Chapter 16). This has been done in order to distinguish the qualitatively different types of solutions. Calculation of the explicit formulas, which describe these geodesics, as well as numerically computed diagrams representing the geodesics have been incorporated in these studies. The following subjects have been also treated: 5. Solutions for the geodesics in Reissner-Nordstrouml;m black holes with |Q_*| gt;= M, which are black holes with one (|Q_*| = M) or no horizon (|Q_*|gt; M) (Chapter 8). 6. Solutions of geodesics in extreme and fast Kerr black holes, i.e. black holes with a = M (extreme) and a gt; M (fast). As in the case of |Q_*| gt; M, fast black holes have naked singularities (Chapter 14). 7. Some general observations about orbit types of the Kerr black holes regarding relationships between parameters such as angular momentum, energy, Carter constant and mass and angular momentum of black holes (Chapter 13). 8. Some corrections to errors found in the literature. While it has not been possible to cover all different cases which occur for possible relations amongst the parameters specifying a general black hole, interesting geodesics have, however, been studied and a more thorough presentation of the properties of geodesics has now been given

Assessment of ultrafine particles in Portuguese preschools: levels and exposure doses

The aim of this work was to assess ultrafine particles (UFP) number concentrations in different microenvironments of Portuguese preschools and to estimate the respective exposure doses of UFP for 3–5-year-old children (in comparison with adults). UFP were sampled both indoors and outdoors in two urban (US1, US2) and one rural (RS1) preschool located in north of Portugal for 31 days. Total levels of indoor UFP were significantly higher at the urban preschools (mean of 1.82x104 and 1.32x104 particles/cm3 at US1 an US2, respectively) than at the rural one (1.15x104 particles/cm3). Canteens were the indoor microenvironment with the highest UFP (mean of 5.17x104, 3.28x104, and 4.09x104 particles/cm3 at US1, US2, and RS1), whereas the lowest concentrations were observed in classrooms (9.31x103, 11.3x103, and 7.14x103 particles/cm3 at US1, US2, and RS1). Mean indoor/outdoor ratios (I/O) of UFP at three preschools were lower than 1 (0.54–0.93), indicating that outdoor emissions significantly contributed to UFP indoors. Significant correlations were obtained between temperature, wind speed, relative humidity, solar radiation, and ambient UFP number concentrations. The estimated exposure doses were higher in children attending urban preschools; 3–5-year-old children were exposed to 4–6 times higher UFP doses than adults with similar daily schedules

Ultrafine Particles in Ambient Air of an Urban Area: Dose Implications for Elderly

Due to their detrimental effects on human health, the scientific interest in ultrafine particles (UFP) has been increasing, but available information is far from comprehensive. Compared to the remaining population, the elderly are potentially highly susceptible to the effects of outdoor air pollution. Thus, this study aimed to (1) determine the levels of outdoor pollutants in an urban area with emphasis on UFP concentrations and (2) estimate the respective dose rates of exposure for elderly populations. UFP were continuously measured over 3 weeks at 3 sites in north Portugal: 2 urban (U1 and U2) and 1 rural used as reference (R1). Meteorological parameters and outdoor pollutants including particulate matter (PM10), ozone (O3), nitric oxide (NO), and nitrogen dioxide (NO2) were also measured. The dose rates of inhalation exposure to UFP were estimated for three different elderly age categories: 64–70, 71–80, and >81 years. Over the sampling period levels of PM10, O3 and NO2 were in compliance with European legislation. Mean UFP were 1.7 × 104 and 1.2 × 104 particles/cm3 at U1 and U2, respectively, whereas at rural site levels were 20–70% lower (mean of 1 ×104 particles/cm3). Vehicular traffic and local emissions were the predominant identified sources of UFP at urban sites. In addition, results of correlation analysis showed that UFP were meteorologically dependent. Exposure dose rates were 1.2- to 1.4-fold higher at urban than reference sites with the highest levels noted for adults at 71–80 yr, attributed mainly to higher inhalation rates

Indoor air quality in health clubs: Impact of occupancy and type of performed activities on exposure levels

Associations between indoor air quality (IAQ) and health in sport practise environments are not well understood due to limited knowledge of magnitude of inhaled pollutants. Thus, this study assessed IAQ in four health clubs (HC1-HC4) and estimated inhaled doses during different types of activities. Gaseous (TVOCs, CO, O3, CO2) and particulate pollutants (PM1, PM4) were continuously collected during 40 days. IAQ was influenced both by human occupancy and the intensity of the performed exercises. Levels of all pollutants were higher when clubs were occupied (p < 0.05) than for vacant periods, with higher medians in main workout areas rather than in spaces/studios for group activities. In all spaces, TVOCs highly exceeded legislative limit (600 μg/m3), even when unoccupied, indicating possible risks for the respective occupants. CO2 levels were well correlated with relative humidity (rs 0.534-0.625) and occupancy due to human exhalation and perspiration during exercising. Clubs with natural ventilations exhibited twice higher PM, with PM1 accounting for 93-96% of PM4; both PM were highly correlated (rs 0.936-0.995) and originated from the same sources. Finally, cardio classes resulted in higher inhalation doses than other types of exercising (1.7-2.6).This work was supported by European Union (FEDER funds through COMPETE) and National Funds (Fundação para a Ciência e Tecnologia) through projects UID/QUI/50006/2013 and UID/EQU/00511/2013-LEPABE, by FCT/MEC with national funds and co-funded by FEDER in the scope of the P2020 Partnership Agreement. Additional financial support was provided by FCT through fellowship SFRH/BPD/105100/2014.info:eu-repo/semantics/publishedVersio

(Ultra) Fine particle concentrations and exposure in different indoor and outdoor microenvironments during physical exercising

Although regular exercise improves overall well-being, increased physical activity results in enhanced breathing which consequently leads to elevated exposure to a variety of air pollutants producing adverse effects. It is well-known that one of these ambient air contaminants is ultrafine particles (UFP). Thus, this study aimed to (1) examine exposure to particle number concentrations (PNC) in size ranging from N20-1000 nm in different sport environments and (2) estimate the respective inhalation doses across varying activity scenarios based upon the World Health Organization recommendations for physical activity. PNC were continuously monitored (TSI P-Trak™ condensation particle counter) outdoors (Out1-Out2) and indoors (Ind1-Ind2; fitness clubs) over 4 weeks. Outdoor PNC (total median 12 563 # cm-3; means of 20 367 # cm-3 at Out1 and 7 122 # cm-3 at Out2) were approximately 1.6-fold higher than indoors (total median 7 653 # cm-3; means of 11 861 # cm-3 at Ind1 and 14 200 # cm-3 at Ind2). The lowest doses were inhaled during holistic group classes (7.91 × 107-1.87 × 108 # per kg body weight) whereas exercising with mixed cardio and strength training led to approximately 1.8-fold higher levels. In order to optimize the health benefit of exercises, environmental characteristics of the locations at which physical activities are conducted need to be considered.This work was financially supported by project UID/EQU/00511/2019 - Laboratory for Process Engineering Environment, Biotechnology and Energy–LEPABE and project UID/QUI/50006/2019 - Associate Laboratory Research Unit for Green Chemistry - Technologies and Processes Clean–LAQV, funded by national funds throughFCT/MCTES (PIDDAC).info:eu-repo/semantics/publishedVersio

Children environmental exposure to particulate matter and polycyclic aromatic hydrocarbons and biomonitoring in school environments: A review on indoor and outdoor exposure levels, major sources and health impacts

Children, an important vulnerable group, spend most of their time at schools (up to 10 h per day, mostly indoors) and the respective air quality may significantly impact on children health. Thus, this work reviews the published studies on children biomonitoring and environmental exposure to particulate matter (PM) and polycyclic aromatic hydrocarbons (PAHs) at school microenvironments (indoors and outdoors), major sources and potential health risks. A total of 28, 35, and 31% of the studies reported levels that exceeded the international outdoor ambient air guidelines for PM10, PM2.5, and benzo(a)pyrene, respectively. Indoor and outdoor concentrations of PM10 at European schools, the most characterized continent, ranged between 7.5 and 229 μg/m3 and 21-166 μg/m3, respectively; levels of PM2.5 varied between 4 and 100 μg/m3 indoors and 6.1-115 μg/m3 outdoors. Despite scarce information in some geographical regions (America, Oceania and Africa), the collected data clearly show that Asian children are exposed to the highest concentrations of PM and PAHs at school environments, which were associated with increased carcinogenic risks and with the highest values of urinary total monohydroxyl PAH metabolites (PAH biomarkers of exposure). Additionally, children attending schools in polluted urban and industrial areas are exposed to higher levels of PM and PAHs with increased concentrations of urinary PAH metabolites in comparison with children from rural areas. Strong evidences demonstrated associations between environmental exposure to PM and PAHs with several health outcomes, including increased risk of asthma, pulmonary infections, skin diseases, and allergies. Nevertheless, there is a scientific gap on studies that include the characterization of PM fine fraction and the levels of PAHs in the total air (particulate and gas phases) of indoor and outdoor air of school environments and the associated risks for the health of children. There is a clear need to improve indoor air quality in schools and to establish international guidelines for exposure limits in these environments.info:eu-repo/semantics/publishedVersio