Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein-Maxwell-charged scalar field system in spherical symmetry which are exactly isometric to extremal Reissner-Nordstr\"om after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. In particular, our result can be viewed as a definitive disproof of the "third law of black hole thermodynamics." The main step in the construction is a novel $C^k$ characteristic gluing procedure, which interpolates between a light cone in Minkowski space and a Reissner-Nordstr\"om event horizon with specified charge to mass ratio $e/M$. Our setup is inspired by the recent work of Aretakis-Czimek-Rodnianski on perturbative characteristic gluing for the Einstein vacuum equations. However, our construction is fundamentally nonperturbative and is based on a finite collection of scalar field pulses which are modulated by the Borsuk-Ulam theorem.Comment: Final version, 46 pages + references, 14 figure

Extremal black hole formation as a critical phenomenon

In this paper, we prove that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal black hole. Physically, these solutions can be understood as beams of gravitationally self-interacting collisionless charged particles fired into Minkowski space from past infinity. Depending on the precise value of the parameter, we show that the Vlasov matter either disperses due to the combined effects of angular momentum and electromagnetic repulsion, or undergoes gravitational collapse. At the critical value of the parameter, an extremal Reissner-Nordstr\"om black hole is formed. No naked singularities occur as the extremal threshold is crossed. We call this critical phenomenon extremal critical collapse and the present work constitutes the first rigorous result on the black hole formation threshold in general relativity.Comment: 91 pages + references, 16 figure

Home and Business Energy Reduction

Course Code: ENR/AEDE 4567The focus of our project is to reduce energy consumption community-wide by 20% over the next five years within the residential and commercial sectors. This 20% reduction is a goal within Green Memo III, set forth by the City of Columbus and Mayor Michael B. Coleman. Focusing on five objectives, we conducted research, gathered data on best practices from cities that have been making strides in this area, reached out to key energy providers, and provided a cost-benefit analysis on the financial feasibility of our goals. We hope to advise Columbus decision makers on how to effectively target homes and commercial buildings in order to market energy efficiency programs. We believe these programs will effectively reduce overall energy consumption and greenhouse gas (GHG) emissions for the City of Columbus.Academic Major: Environment, Economy, Development, and Sustainabilit

Immunofluorescence Visualization of Polycyclic Aromatic Hydrocarbon Mixtures in the Eastern Oyster Crassostrea virginica

Bivalve mollusks including oysters have low metabolic potential and are therefore susceptible to accumulating high levels of lipophilic organic contaminants such as polycyclic aromatic hydrocarbons (PAHs). Human exposure to PAHs via consumption of this important commercial shellfish can be a serious public health concern in areas where high PAH contamination exists. Previous PAH immunohistochemical studies have been limited to laboratory-based exposures focusing on one or a few individual PAH compounds. To date, such studies have yet to explore PAH accumulation in oysters, known to have some of the highest levels of PAHs across different food products. Using a monoclonal antibody selective for a range of three- to five-ring PAHs, we present a method to detect and localize complex mixtures of PAHs in oyster tissues via fluorescent immunohistochemistry. Observed immunofluorescence intensity followed a similar trend as measured levels of PAHs in oyster interstitial fluid from PAH-contaminated sites and oysters exposed to the water accommodated fraction of crude oil. This method will be valuable in understanding internal partitioning mechanisms of PAH-exposed oysters and will have important applications in studies on PAH distribution in the tissues of additional organisms for environmental, medical, or veterinary purposes

Evaluating Interactive Transect Area Assessments Hands-On Instruction for Natural Resource Undergraduate Students

Undergraduate students pursuing a Bachelor of Science in Spatial Science degree at Stephen F. Austin State University (SFASU) receive instruction in the spatial sciences with a focus on hands-on applications. All undergraduate students take the course Introduction to Spatial Science which includes a comprehensive overview of spatial science incorporating a comparison of standard inexpensive area assessment techniques with high-end computer based area assessment methodologies. Students within this course were instructed how to assess the area of a surface feature on an aerial image with a ruler applying the transect method. Student\u27s average Root Mean Square Error (RMSE) between a student\u27s transect derived area and surveyed area was 0.45, 0.13, 0.07, and 0.02 acres for 5, 10, 15, and 20 transect lines, respectfully. An ANOVA analysis of area assessment and area error assessment indicated that mean area and mean absolute area error were statistically different between transect line groups. In addition, the accuracy of area measured increased significantly as the number of transect lines increased which: (1) indicates students receiving hands-on instruction in estimating area using the transect method can record accurate area measurements after only a limited 2 hour introduction; (2) reveals the accuracy of the transect method is not user dependent; (3) shows area accuracy increases as the number of transects increases; and, (4) validates the interactive hands-on instruction methodology employed at SFASU

Surface velocity fluctuations for Glaciar Universidad, central Chile, between 1967 and 2015

For the Andes Cordillera, where observed mass-balance records are sparse, long-term glacier velocity measurements potentially represent a useful tool for assessing glacier health. Utilising manual and automatic feature-tracking techniques applied to Corona, Landsat and ASTER satellite imagery, this paper presents surface velocity fluctuations for Glaciar Universidad between 1967 and 1969, and 1985 and 2015, the longest such time series available for the Andes Cordillera, outside Patagonia. This time series reveals an increase in the surface velocities of the main glacier trunk between 1967 and 1987 (~90%) followed by a deceleration between 1987 and 2015 (~80%), with ice velocities observed between 2014 and 2015 possibly representing a 48 a low. In response to the surface velocity fluctuations, the glacier front advanced between 1985 and 1992 (cumulative change of 137 ± 14 m), and again to a lesser magnitude during the 1996–98 and 2004–08 periods. Although having exhibited possible surge behaviour during the 1940s, the synchrony of the glacier changes presented for Glaciar Universidad with those reported for nearby glaciers, suggests that this glacier is responding to climatic trends. If the above scenario is true, the results indicate a general pattern of increasingly negative glacier mass-balance conditions since the late 1980

CarboScen : A tool to estimate carbon implications of land-use scenarios

Land use directly impacts ecosystem carbon and indirectly influences atmospheric carbon. Computing ecosystem carbon for an area experiencing changes in land use is not trivial, as carbon densities change slowly after land-use changes. We developed a tool, CarboScen, to estimate ecosystem carbon in landscapes. It is a simple tool typically used with an annual time step, and is based on carbon pools and densities. It assumes that carbon density asymptotically approaches a value, which is set for the land-use type in question. We recommend CarboScen for landscapes with spatially relatively homogenous soils and climate, multiple land uses, and changes between these leading to slow changes in carbon densities because either soil organic carbon is included in the analysis or afforestation occurs. Thanks to its simplicity, it is particularly suitable for participatory planning, rapid assessment of REDD+ project potential, and educational use.Peer reviewe