SHORTCUT METHOD OF SOLUTION OF GEODESIC EQUATIONS FOR SCHWARZSCHILD BLACK HOLE

It is shown how the use of the Kerr-Schild coordinate system can greatly simplify the formulation of the geodesic equation of the Schwarzschild solution. An application of this formulation to the numerical computation of the aspect of a non-rotating black hole is presented. The generalization to the case of the Kerr solution is presented too.Comment: 11 pages, 2 PostScript figures (available as uuencoded compressed tar file), uses epsfig.tex). Accepted on February 1995 for publication in Classical and Quantum Gravit

Numerical approach for high precision 3-D relativistic star models

A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error reveals to be of the order of $10^{-10}$. This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres

Numerical models of irrotational binary neutron stars in general relativity

We report on general relativistic calculations of quasiequilibrium configurations of binary neutron stars in circular orbits with zero vorticity. These configurations are expected to represent realistic situations as opposed to corotating configurations. The Einstein equations are solved under the assumption of a conformally flat spatial 3-metric (Wilson-Mathews approximation). The velocity field inside the stars is computed by solving an elliptical equation for the velocity scalar potential. Results are presented for sequences of constant baryon number (evolutionary sequences). Although the central density decreases much less with the binary separation than in the corotating case, it still decreases. Thus, no tendency is found for the stars to individually collapse to black hole prior to merger.Comment: Minor corrections, improved figure, 5 pages, REVTeX, Phys. Rev. Lett. in pres

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests

We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multi-domain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multi-domain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in details for a polytropic equation of state with gamma=2.Comment: Minor corrections, references updated, 42 pages, 25 PostScript figures, accepted for publication in Phys. Rev.

Mortality in Female and Male French Olympians

International audienceBackground: Whereas intense physical activity has been associated with deleterious effects on elite athletes' health, in particular due to cardiovascular anomalies, long-term follow-ups have suggested lower mortality rates among elite athletes. Causes of death for French Olympic athletes and female elite athletes have not been studied.Hypothesis/Purpose: We aimed to measure overall and disease-specific mortality of French female and male Olympians comparedwith the French general population. We hypothesize that Olympians, both women and men, have lower mortality rates.Study Design: Cohort study; Level of evidence, 3.Methods: French elite athletes (601 women and 1802 men) participating in summer or winter Olympic Games from 1948 to 2010had their vital status verified by national sources and were followed until 2013. Causes of death were obtained via the NationalDeath registry from 1968 to 2012. Overall and disease-specific mortalities of Olympians were compared with those of the Frenchgeneral population through standardized mortality ratios (SMRs) and 95% CIs. Olympians’ observed and expected survivals wereillustrated by Kaplan-Meier curves.Results: At the endpoint of the study, 13 women and 222 men had died. Overall mortality in Olympians compared with that oftheir compatriots was 51% lower (SMR, 0.49; 95% CI, 0.26-0.85) among women and 49% lower (SMR, 0.51; 95% CI, 0.45-0.59) among men. Olympic athletes’ survival is significantly superior to that of the French general population (women, P = .03;men, P\.001). According to the total deaths occurring from 1968 to 2012 (12 among women, 202 among men), female Olympiansdied from neoplasm (50.0%), external causes (33.3%), and cardiovascular diseases (16.6%). The main causes of deathamong men were related to neoplasms (36.1%), cardiovascular diseases (24.3%), and external causes (14.4%). Regarding themain causes of mortality among male Olympic athletes, the SMRs were as follows: 0.55 for neoplasms (95% CI, 0.43-0.69),0.55 for cardiovascular diseases (95% CI, 0.41-0.73), and 0.66 for external causes (95% CI, 0.44-0.94).Conclusion: French Olympians live longer than their compatriots: A lower overall mortality of similar magnitude is observedamong male and female athletes compared with the general population. The main causes of death in French Olympians are neoplasms, cardiovascular diseases, and external causes