A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.Comment: Contribution to the "Encuentros Relativistas Espanoles - Spanish Relativity Meeting ERE07" Proceedings, Tenerife, Spain (September 2007

The Goldberg-Sachs theorem in linearized gravity

The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized solutions.Comment: 6 pages, no figures, LaTeX 2

Conformally flat black hole initial data, with one cylindrical end

We give a complete analytical proof of existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and extreme Bowen-York's initial data. This extends and refines a previous result \cite{dain-gabach09} to a general case of conformally flat, maximal initial data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published version in Class. Quantum Grav. (2010). Results unchange

Initial data for fluid bodies in general relativity

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.JrComment: 38 pages, LaTeX 2e, no figures. Accepted for publication in Phys. Rev.

Excess Body Weight and Gait Influence Energy Cost of Walking in Older Adults

Purpose: To study how excess body weight influences the energy cost of walking (Cw) and determine if overweight and obese older adults self-select stride frequency to minimize Cw. Methods: Using body mass index (BMI) men and women between the ages of 65–80 yr were separated into normal weight (NW, BMI ≤ 24.9 kg m−2, n = 13) and overweight-obese groups (OWOB, BMI ≥25.0 kg m−2, n = 13). Subjects walked at 0.83 m s−1 on an instrumented treadmill that recorded gait parameters, and completed three, six-minute walking trials; at preferred stride frequency (PSF), at +10% PSF, and at −10% PSF. Cw was determined by indirect calorimetry. Repeated measures analysis of variance was used to compare groups, and associations were tested with Pearson correlations, α = 0.05. Results: OWOB had 62% greater absolute Cw (301 ± 108 vs. 186 ± 104 J m−1, P \u3c 0.001) and 20% greater relative Cwkg (3.48 ± 0.95 vs. 2.91 ± 0.94 J kg−1 m−1, P = 0.046) than NW. Although PSF was not different between OWOB and NW (P = 0.626), Cw was 8% greater in OWOB at +10% PSF (P \u3c 0.001). At PSF OWOB spent less time in single-limb support (33.1 ± 1.5 vs. 34.9 ± 1.6 %GC, P = 0.021) and more time in double-limb support (17.5 ± 1.6 vs. 15.4 ± 1.4 %GC, P = 0.026) than NW. In OWOB, at PSF, Cw was correlated to impulse (r = −0.57, P = 0.027) and stride frequency (r = 0.51, P = 0.046). Conclusions: Excess body weight is associated with greater Cw in older adults, possibly contributing to reduced mobility in overweight and obese older persons

Existence and uniqueness of Bowen-York Trumpets

We prove the existence of initial data sets which possess an asymptotically flat and an asymptotically cylindrical end. Such geometries are known as trumpets in the community of numerical relativists.Comment: This corresponds to the published version in Class. Quantum Grav. 28 (2011) 24500

Descriptive Analysis of a Baseline Concussion Battery Among U.S. Service Academy Members: Results from the Concussion Assessment, Research, and Education (CARE) Consortium

Introduction The prevalence and possible long-term consequences of concussion remain an increasing concern to the U.S. military, particularly as it pertains to maintaining a medically ready force. Baseline testing is being used both in the civilian and military domains to assess concussion injury and recovery. Accurate interpretation of these baseline assessments requires one to consider other influencing factors not related to concussion. To date, there is limited understanding, especially within the military, of what factors influence normative test performance. Given the significant physical and mental demands placed on service academy members (SAM), and their relatively high risk for concussion, it is important to describe demographics and normative profile of SAMs. Furthermore, the absence of available baseline normative data on female and non-varsity SAMs makes interpretation of post-injury assessments challenging. Understanding how individuals perform at baseline, given their unique individual characteristics (e.g., concussion history, sex, competition level), will inform post-concussion assessment and management. Thus, the primary aim of this manuscript is to characterize the SAM population and determine normative values on a concussion baseline testing battery. Materials and Methods All data were collected as part of the Concussion Assessment, Research and Education (CARE) Consortium. The baseline test battery included a post-concussion symptom checklist (Sport Concussion Assessment Tool (SCAT), psychological health screening inventory (Brief Symptom Inventory (BSI-18) and neurocognitive evaluation (ImPACT), Balance Error Scoring System (BESS), and Standardized Assessment of Concussion (SAC). Linear regression models were used to examine differences across sexes, competition levels, and varsity contact levels while controlling for academy, freshman status, race, and previous concussion. Zero inflated negative binomial models estimated symptom scores due to the high frequency of zero scores. Results Significant, but small, sex effects were observed on the ImPACT visual memory task. While, females performed worse than males (p < 0.0001, pη2 = 0.01), these differences were small and not larger than the effects of the covariates. A similar pattern was observed for competition level on the SAC. There was a small, but significant difference across competition level. SAMs participating in varsity athletics did significantly worse on the SAC compared to SAMs participating in club or intramural athletics (all p’s < 0.001, η2 = 0.01). When examining symptom reporting, males were more than two times as likely to report zero symptoms on the SCAT or BSI-18. Intramural SAMs had the highest number of symptoms and severity compared to varsity SAMs (p < 0.0001, Cohen’s d < 0.2). Contact level was not associated with SCAT or BSI-18 symptoms among varsity SAMs. Notably, the significant differences across competition level on SCAT and BSI-18 were sub-clinical and had small effect sizes. Conclusion The current analyses provide the first baseline concussion battery normative data among SAMs. While statistically significant differences may be observed on baseline tests, the effect sizes for competition and contact levels are very small, indicating that differences are likely not clinically meaningful at baseline. Identifying baseline differences and significant covariates is important for future concussion-related analyses to inform concussion evaluations for all athlete levels

Geometric inequalities for axially symmetric black holes

A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse, they are closed related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problem is presented.Comment: 65 pages, 5 figures. Review article, to appear in Class. Quantum Grav. as Topical Review. Improved presentation, minor corrections, references updat

Initial data for two Kerr-like black holes

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of one of them is zero, this family reduces exactly to the Kerr initial data. The existence proof is based on a general property of the Kerr metric which can be used in other constructions as well. Further generalizations are also discussed.Comment: revtex, 5 pages, no figure