General Relativistic Hydrodynamic Equations in Multiple Coordinates

Details General Relativistic Hydrodynamic Equations in Multiple Coordinates General Relativistic Hydrodynamic Equations in Multiple Coordinates

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet..983w&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

General relativistic hydrodynamics is an important subject in classical general relativity1. The importance is not only from theoretical point view, but also in the practical application, e.g., compact star, precise measurement in geophysics and cosmological problems. For first order post-Newtonian (1PN) hydrodynamics it has been investigated by many authors (e.g. Chandrasekhar2; Greenberg3; Blanchet, Damour & Schäfer4). But we should point out most of the calculations are in one-global coordinate, or we should call them as one coordinate hydrodynamics. Only in very few cases5, they considered the hydrodynamic equations of the perfect fluid in local coordinate by means of matching technic6. As we know, the calculation of matching technic is quite long and complex. Up to now, no one has consider a complete hydrodynamic equations of nonperfect fluid and the corresponding thermodynamic equations in multiple coordinates. In some cases, e.g. in binary or N-body system, stars in globular cluster et al., it is necessary to introduce a local coordinate system for each object to calculate local multipole moments7. So we shall deal with hydrodynamic problem in multiple coordinates.

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