GT3 - Einstein-Maxwell Systems |
Speaker_ |
Daishev, Rinat |
Talk _ |
Equilibrium distributions of charged fluid in the space-times with the groups of homothetic |
Abstract _ |
Space-times $\;V_4,\;$ admitting a groups of homothetic motions $\;H_r\;$ with the charged fluid as its source are discussed. It is assumed that the vector of velocity of the fluid is collinear to the time-like vector $\;Y\;$ of the group's Lie algebra. We prove that if $\;(\rho + 3p) \not=0,\;$ the vector $\;Y\;$ is the vector of the Lie algebra, corresponding to isometric transformations of the group $\;H_r\;$ and giving rise to time-like ideal of the Lie algebra of the group $\;H_r.\;$ All space-times $\;V_4,\;$ admitting a groups of homothetic transformations with indicated properties, are selected. Equations $\;(T^{ik}+E^{ik})_{\vert k} = 0\;$ are integrated entirely, and all possible equations of state of investigated fluid are presented.It is founded that pressure, energy density and electrical charges density expressed solely through field quantities. |