Abstract
The present paper is concerned with the conservation laws in general relativity as expressed in terms of the Landau-Lifshitz complex and their role in the development of the successive post-Newtonian approximations to the equations of general relativity of a perfect fluid. In § I, the known conservation laws of Newtonian hydrodynamics are formulated in a language that the relativistic laws appear as natural generalizations. In § II, the same laws are considered in the framework of general relativity. In particular the conserved energy is identified as the difference between the (0,0)-component of the Landau-Lifshitz complex and the conserved rest-mass energy (\(={{c}^{2}}p{{u}^{0}}\sqrt{-g}\)). In § III, the development of the first and the second post-Newtonian approximations to the equations of relativistic hydrodynamics are described and illustrated. And finally in § IV, the manner in which one can obtain the equations of the 2 1/2 — post-Newtonian approximation is described. In this approximation all terms inclusive of O(c−5) beyond the Newtonian are retained; it is in this approximation that terms representing the reaction of the fluid to the emission of gravitational radiation by the system first make their appearance. It is shown how the derived radiation-reaction terms of O(c−5) contribute to the dissipation of energy and angular momentum in agreement with the predictions of the linearized theory of gravitational radiation.
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© 1970 Plenum Press, New York
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Chandrasekhar, S. (1970). Post-Newtonian Methods and Conservation Laws. In: Carmeli, M., Fickler, S.I., Witten, L. (eds) Relativity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-0721-1_6
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DOI: https://doi.org/10.1007/978-1-4684-0721-1_6
Publisher Name: Springer, Boston, MA
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