Area Invariance of Apparent Horizons under Arbitrary Boosts

It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the $t=constant$ slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the Kerr-Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider {\it boosted} versions with the black hole moving through the coordinate system. Since these are stationary black hole spacetimes, the apparent horizons are two dimensional cross sections of their event horizons, so we compute the areas of apparent horizons in the boosted space with (boosted) $t = constant$, and obtain the same result as in the unboosted case. Note that while the invariance of area is generic, we deal only with black holes in the Kerr-Schild form, and consider only one particularly simple change of slicing which amounts to a boost. Even with these restrictions we find that the results illuminate the physics of the horizon as a null surface and provide a useful pedagogical tool. As far as we can determine, this is the first explicit calculation of this type demonstrating the area invariance of horizons. Further, these calculations are directly relevant to transformations that arise in computational representation of moving black holes. We present an application of this result to initial data for boosted black holes.Comment: 19 pages, 3 figures. Added a new section and 2 plots along with a coautho

On the Singularity Structure and Stability of Plane Waves

We describe various aspects of plane wave backgrounds. In particular, we make explicit a simple criterion for singularity by establishing a relation between Brinkmann metric entries and diffeomorphism-invariant curvature information. We also address the stability of plane wave backgrounds by analyzing the fluctuations of generic scalar modes. We focus our attention on cases where after fixing the light-cone gauge the resulting world sheet fields appear to have negative "mass terms". We nevertheless argue that these backgrounds may be stable.Comment: 21 pages, 1 figur

Gauge and Scheme Dependence of Mixing Matrix Renormalization

We revisit the issue of mixing matrix renormalization in theories that include Dirac or Majorana fermions. We show how a gauge-variant on-shell renormalized mixing matrix can be related to a manifestly gauge-independent one within a generalized ${\bar {\rm MS}}$ scheme of renormalization. This scheme-dependent relation is a consequence of the fact that in any scheme of renormalization, the gauge-dependent part of the mixing-matrix counterterm is ultra-violet safe and has a pure dispersive form. Employing the unitarity properties of the theory, we can successfully utilize the afore-mentioned scheme-dependent relation to preserve basic global or local symmetries of the bare Lagrangian through the entire process of renormalization. As an immediate application of our study, we derive the gauge-independent renormalization-group equations of mixing matrices in a minimal extension of the Standard Model with isosinglet neutrinos.Comment: 31 pages, LaTeX, uses axodraw.st

Characteristics, Outcomes, and Severity Risk Factors Associated with SARS-CoV-2 Infection among Children in the US National COVID Cohort Collaborative

Importance: Understanding of SARS-CoV-2 infection in US children has been limited by the lack of large, multicenter studies with granular data. Objective: To examine the characteristics, changes over time, outcomes, and severity risk factors of children with SARS-CoV-2 within the National COVID Cohort Collaborative (N3C). Design, Setting, and Participants: A prospective cohort study of encounters with end dates before September 24, 2021, was conducted at 56 N3C facilities throughout the US. Participants included children younger than 19 years at initial SARS-CoV-2 testing. Main Outcomes and Measures: Case incidence and severity over time, demographic and comorbidity severity risk factors, vital sign and laboratory trajectories, clinical outcomes, and acute COVID-19 vs multisystem inflammatory syndrome in children (MIS-C), and Delta vs pre-Delta variant differences for children with SARS-CoV-2. Results: A total of 1068410 children were tested for SARS-CoV-2 and 167262 test results (15.6%) were positive (82882 [49.6%] girls; median age, 11.9 [IQR, 6.0-16.1] years). Among the 10245 children (6.1%) who were hospitalized, 1423 (13.9%) met the criteria for severe disease: mechanical ventilation (796 [7.8%]), vasopressor-inotropic support (868 [8.5%]), extracorporeal membrane oxygenation (42 [0.4%]), or death (131 [1.3%]). Male sex (odds ratio [OR], 1.37; 95% CI, 1.21-1.56), Black/African American race (OR, 1.25; 95% CI, 1.06-1.47), obesity (OR, 1.19; 95% CI, 1.01-1.41), and several pediatric complex chronic condition (PCCC) subcategories were associated with higher severity disease. Vital signs and many laboratory test values from the day of admission were predictive of peak disease severity. Variables associated with increased odds for MIS-C vs acute COVID-19 included male sex (OR, 1.59; 95% CI, 1.33-1.90), Black/African American race (OR, 1.44; 95% CI, 1.17-1.77), younger than 12 years (OR, 1.81; 95% CI, 1.51-2.18), obesity (OR, 1.76; 95% CI, 1.40-2.22), and not having a pediatric complex chronic condition (OR, 0.72; 95% CI, 0.65-0.80). The children with MIS-C had a more inflammatory laboratory profile and severe clinical phenotype, with higher rates of invasive ventilation (117 of 707 [16.5%] vs 514 of 8241 [6.2%]; P <.001) and need for vasoactive-inotropic support (191 of 707 [27.0%] vs 426 of 8241 [5.2%]; P <.001) compared with those who had acute COVID-19. Comparing children during the Delta vs pre-Delta eras, there was no significant change in hospitalization rate (1738 [6.0%] vs 8507 [6.2%]; P =.18) and lower odds for severe disease (179 [10.3%] vs 1242 [14.6%]) (decreased by a factor of 0.67; 95% CI, 0.57-0.79; P <.001). Conclusions and Relevance: In this cohort study of US children with SARS-CoV-2, there were observed differences in demographic characteristics, preexisting comorbidities, and initial vital sign and laboratory values between severity subgroups. Taken together, these results suggest that early identification of children likely to progress to severe disease could be achieved using readily available data elements from the day of admission. Further work is needed to translate this knowledge into improved outcomes

Customer emotions in service failure and recovery encounters

Emotions play a significant role in the workplace, and considerable attention has been given to the study of employee emotions. Customers also play a central function in organizations, but much less is known about customer emotions. This chapter reviews the growing literature on customer emotions in employee–customer interfaces with a focus on service failure and recovery encounters, where emotions are heightened. It highlights emerging themes and key findings, addresses the measurement, modeling, and management of customer emotions, and identifies future research streams. Attention is given to emotional contagion, relationships between affective and cognitive processes, customer anger, customer rage, and individual differences

Equation of State of Classical Systems of Charged Particles

Recent developments in the classical theory of fully ionized gases and strong electrolyte solutions are reviewed, and are used to discuss the equation of state at high temperatures and low densities. The pressure is calculated using the ring-integral approximation, and quantitative estimates of higher correction terms are given. The effect of short range repulsive forces is shown by comparing the results with two kinds of potential functions hard spheres of diameter a, and soft'' spheres for which the short range potential cancels the Coulomb potential at the origin, and decreases exponentially with distance. It is found that the use of either type of potential extends the range of validity of the ring-integral approximation to considerably higher densities and lower temperatures. Since there is little difference in the results for the hard spheres and the soft spheres in this range, the latter system is investigated more extensively since it is more, easily handled by analytical methods. The expressions derived for the free energy of a system of charged particles can also be used in ionization equilibrium calculations, and the effect of electrostatic interactions on the equilibrium concentrations of various kinds of ions is indicated. 60 references. (auth