Chandrasekhar, S. ; Paul Esposito, F. (1970) The 2½postNewtonian equations of hydrodynamics and radiation reaction in general relativity Astrophysical Journal, 160 . pp. 153179. ISSN 0004637X

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Official URL: http://adsabs.harvard.edu/abs/1970ApJ...160..153C
Related URL: http://dx.doi.org/10.1086/150414
Abstract
In this paper the equations of hydrodynamics in the 2½postNewtonian approximation to general relativity are derived. In this approximation all terms of O(c^{5}) are retained consistently with Einstein's field equations; it is also the approximation in which terms representing the reaction of the fluid to the emission of gravitational radiation by the system first make their appearance. The paper is in four parts. In Part I (by S. C.) the lowestorder terms in the metric coefficients are derived which are consequences of the imposition of the Sommerfeld radiationcondition at infinity. It is shown (following an early investigation of Trautman) that these terms are of O(c^{5}) in g_{00}, of O(c^{6}) in g_{0α}, and of O(c^{5}) in g_{αβ}. Unique expressions are obtained for these terms. They are found to be purely of Newtonian origin. In Part II (by S. C. and F. P. E.) the equations of motion governing the fluid in the 2½postNewtonian approximation are derived. In addition to the coefficients already determined, these equations depend on a knowledge of the term of O(c^{7}) in g_{oo}. This term is determined by an explicit appeal to the field equation. It is further shown that this approximation brings no change to the density (c^{2}ρμ^{0}√g) and the linear momentum (π_{α}) that are conserved in the second postNewtonian approximation. In Part III (by S. C.) it is shown that the terms of O(c^{5}) in the equations of motion contribute principally to the dissipation of the energy and the angular momentum conserved in the second postNewtonian approximation. The rates of dissipation of energy and of angular momentum that are predicted are in exact agreement with the expectations of the linearized theory of gravitational radiation. Finally, in Part IV (by S. C. and F. P. E.) the energy, θ^{00}c^{2}ρμ^{0}√g, to be associated with the 2½postNewtonian approximation is derived by evaluating the (0, 0)component of the LandauLifshitz complex and the conserved density in the 3½postNewtonian approximation.
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