Schwarzschild Space-Time in Gauge Theories of Gravity

In Poincar\'e gauge theory of gravity and in \overline{\mbox{Poincar\'e}} gauge theory of gravity, we give the necessary and sufficient condition in order that the Schwarzschild space-time expressed in terms of the Schwarzschild coordinates is obtainable as a torsionless exact solution of gravitational field equations with a spinless point-like source having the energy-momentum density \widetilde{\mbox{\boldmath T}}_\mu^{~\nu}(x) = - Mc^2 \delta_\mu^{~0} \delta_0^{~\nu} \delta^{(3)}(\mbox{\boldmath x}). Further, for the case when this condition is satisfied, the energy-momentum and the angular momentum of the Schwarzschild space-time are examined in their relations to the asymptotic forms of vierbein fields. We show, among other things, that asymptotic forms of vierbeins are restricted by requiring the equality of the active gravitational mass and the inertial mass. Conversely speaking, this equality is violated for a class of vierbeins giving the Schwarzschild metric.Comment: 26 pages, LaTeX, uses amssymb.sty. To appear in Prog. Theor. Phys. 99 (1998

Distributional Energy-Momentum Densities of Schwarzschild Space-Time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\tilde T_\mu^{\nu}(x)$ of the gravitational source and the gravitational energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions $\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and $\tilde t_\mu^{\nu}=0$, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like $\delta^{(3)}(x)/r^3$ and [\delta^{(3)}(x)}]^2, as well as other terms, which are singular at $x=0$. It is pointed out that the well-known expression $R^{\rho\sigma\mu\nu}({}) R_{\rho\sigma\mu\nu}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$ is not correct, if we define $1/r^6 = \lim_{\epsilon\to 0}1/(r^2+\epsilon^2)^3$.}Comment: 21 pages, LaTeX, uses amssymb.sty. To appear in Prog. Theor. Phys. 98 (1997

PetaFlow: a global computing-networking-visualisation unitwith social impact

International audienceThe PetaFlow application aims to contribute to the use of high performance computational resources forthe benefit of society. To this goal the emergence of adequate information and communication technologies withrespect to high performance computing-networking-visualisation and their mutual awareness is required. Thedeveloped technology and algorithms are presented and applied to a real global peta-scale data intensive scientificproblem with social and medical importance, i.e. human upper airflow modelling

Distributional Energy-Momentum Densities of Schwarzschild Space-Time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of KerrSchild types as special cases. The energy-momentum density e T ¯ (x) of the gravitational source and the gravitational energy-momentum pseudo-tensor density e t ¯ have the expressions e T ¯ (x) = \GammaM c 2 ffi 0 ¯ ffi 0 ffi (3) (x) and e t ¯ = 0, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like ffi (3) (x)=r 3 and \Theta ffi (3) (x) 2 , as well as other terms, which are singular at x = 0. It is pointed out that the well-known expression R aeoe¯ (fg)R aeoe¯ (fg) = 48G 2 M 2 =c 4 r 6 is not correct, if we define 1=r 6 def = lim ffl!0 1=(r 2 + ffl 2 ) 3 . Electronic address: [email protected] y Electronic address: sakane@sci...