Sharp bounds on the critical stability radius for relativistic charged spheres

In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M\leq 4R/9, has been found. In this paper we derive the surprisingly transparent inequality $$\sqrt{M}\leq\frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}.$$ The inequality is shown to hold for any solution which satisfies $p+2p_T\leq\rho,$ where $p\geq 0$ and $p_T$ are the radial- and tangential pressures respectively and $\rho\geq 0$ is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.Comment: 20 pages, 1 figur

Thermodynamics Inducing Massive Particles' Tunneling and Cosmic Censorship

By calculating the change of entropy, we prove that the first law of black hole thermodynamics leads to the tunneling probability of massive particles through the horizon, including the tunneling probability of massive charged particles from the Reissner-Nordstr\"om black hole and the Kerr-Newman black hole. Novelly, we find the trajectories of massive particles are close to that of massless particles near the horizon, although the trajectories of massive charged particles may be affected by electromagnetic forces. We show that Hawking radiation as massive particles tunneling does not lead to violation of the weak cosmic-censorship conjecture

Diving into the vertical dimension of elasmobranch movement ecology

Knowledge of the three-dimensional movement patterns of elasmobranchs is vital to understand their ecological roles and exposure to anthropogenic pressures. To date, comparative studies among species at global scales have mostly focused on horizontal movements. Our study addresses the knowledge gap of vertical movements by compiling the first global synthesis of vertical habitat use by elasmobranchs from data obtained by deployment of 989 biotelemetry tags on 38 elasmobranch species. Elasmobranchs displayed high intra- and interspecific variability in vertical movement patterns. Substantial vertical overlap was observed for many epipelagic elasmobranchs, indicating an increased likelihood to display spatial overlap, biologically interact, and share similar risk to anthropogenic threats that vary on a vertical gradient. We highlight the critical next steps toward incorporating vertical movement into global management and monitoring strategies for elasmobranchs, emphasizing the need to address geographic and taxonomic biases in deployments and to concurrently consider both horizontal and vertical movements

Hydronephrosis Classifications : Has UTD Overtaken APD and SFU? A Worldwide Survey

Objective: To collect baseline information on the ultrasonographic reporting preferences. Method: A 13-multiple choice questionnaire was designed and distributed worldwide among pediatric urologists, pediatric surgeons, and urologists. The statistical analysis of the survey data consisted of 3 steps: a univariate analysis, a bivariate and a multivariate analysis. Results: Three hundred eighty participants responded from all the continents. The bivariate analysis showed the significant differences in the geographical area, the years of experience and the volume of cases. Most of the physicians prefer the SFU and APD systems because of familiarity and simplicity (37 and 34%, respectively). Respondents noted that their imaging providers most often report findings utilizing the mild-moderate-severe system or the APD measurements (28 and 39%, respectively) except for North America (SFU in 50%). Multivariate analysis did not provide significant differences. Conclusion: Our study evaluates the opinions regarding the various pediatric hydronephrosis classification systems from a large number of specialists and demonstrates that there is no single preferred grading system. The greatest reported shortcoming of all the systems was the lack of universal utilization. The observations taken from this study may serve as basis for the construction of a common worldwide system. As APD and SFU are the preferred systems and the UTD a newer combination of both, it is possible that with time, UTD may become the universal language for reporting hydronephrosis. This time, based on the result of this survey, seems not arrived yet