Abstract
In the author’s previous publications, a recursive linear algebraic method was introduced for obtaining (without gravitational radiation) the full potential expansions for the gravitational metric field components and the Lagrangian for a general N-body system. Two apparent properties of gravity— Exterior Effacement and Interior Effacement—were defined and fully enforced to obtain the recursive algebra, especially for the motion-independent potential expansions of the general N-body situation. The linear algebraic equations of this method determine the potential coefficients at any order n of the expansions in terms of the lower-order coefficients. Then, enforcing Exterior and Interior Effacement on a selecedt few potential series of the full motion-independent potential expansions, the complete exterior metric field for a single, spherically-symmetric mass source was obtained, producing the Schwarzschild metric field of general relativity. In this fourth paper of this series, the complete spatial metric’s motion-independent potentials for N bodies are obtained using enforcement of Interior Effacement and knowledge of the Schwarzschild potentials. From the full spatial metric, the complete set of temporal metric potentials and Lagrangian potentials in the motion-independent case can then be found by transfer equations among the coefficients κ(n, α) → λ(n, ε) → ξ(n, α) with κ(n, α), λ(n, ε), ξ(n, α) being the numerical coefficients in the spatial metric, the Lagrangian, and the temporal metric potential expansions, respectively.
Similar content being viewed by others
References
K. Nordtvedt, Grav. Cosmol. 21, 123 (2015).
K. Nordtvedt, Grav. Cosmol. 21, 134 (2015).
K. Nordtvedt, Grav. Cosmol. 23, 8 (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Lorentz contraction and time dilation conditions are also used to formulate iterative algebraic equations for the motion-dependent potentials of metric gravity. Such potentials, however, are not a needed part of this paper’s considerations.
Rights and permissions
About this article
Cite this article
Nordtvedt, K. Finding Coefficients of the Full Array of Motion-Independent N-Body Potentials of Metric Gravity from Gravity’s Exterior and Interior Effacement Algebra. Gravit. Cosmol. 24, 46–51 (2018). https://doi.org/10.1134/S0202289318010115
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0202289318010115