Physics
Scientific paper
Aug 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996gregr..28..953z&link_type=abstract
General Relativity and Gravitation, Volume 28, Issue 8, pp.953-979
Physics
7
Scientific paper
The derivation of MacCallum-Taub's averaged high-frequency Lagrangian [1] is analysed with special attention paid to the assumptions made along the derivation. It is shown that averaged high-frequency Lagrangians of the same form as MacCallum-Taub's Lagrangian can be derived by applying the Brill-Hartle and macroscopic gravity averaging schemes. A procedure for the derivation of a Lagrangian of macroscopic gravity (an averaged Hilbert action) is proposed and its high-frequency limit (namely, its high-frequency perturbation expansion up to the second order terms in perturbations, which is referred to as MacCallum-Taub's limit) is calculated. There is disagreement [2] in the expressions for MacCallum-Taub's averaged high-frequency Lagrangian and the high-frequency limit of the macroscopic gravity Lagrangian. Possible reasons for such disagreement are analysed. The origin of the difference is shown to consist in using the propagation equation for perturbations, i.e. the linearized Ricci tensor vanishes, during the derivation (averaging) carried out in [1]. A new derivation of an averaged high-frequency Lagrangian without assuming the propagation equation to hold and by taking into account the proper correlation functions is given. The newly derived expression is shown to coincide with MacCallum-Taub's limit of the macroscopic gravity Lagrangian, which resolves the disagreement.
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