Equations of hydrodynamics in general relativity via a slowmotion expansion of an integral solution
Abstract
By means of a formal solution to the Einstein gravitational field equations a slowmotion expansion in inverse powers of the speed of light is developed for the metric tensor. The formal solution, which satisfies the deDonder coordinate conditions and the Trautman outgoingradiation condition, is in the form of an integral equation which is solved iteratively. A stressenergy tensor appropriate to a perfect fluid is assumed and all orders of the metric needed to obtain the equations of motion and conserved quantities to the 21/2 postNewtonian approximation are found. The results of this method are compared to those previously obtained in another gauge by S. Chandrasekhar. They are shown to be equivalent, but require considerably less labor in their determination. The relation of the fastmotion approximation to the slowmotion approximation is examined.
 Publication:

Ph.D. Thesis
 Pub Date:
 1974
 Bibcode:
 1974PhDT........27D
 Keywords:

 Hydrodynamic Equations;
 Integral Equations;
 Relativity;
 Equations Of Motion;
 Fluid Mechanics;
 Gravitational Fields;
 Tensor Analysis;
 Fluid Mechanics and Heat Transfer