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Bach-Einstein Gravitational Field Equations as a Perturbation of Einstein Gravitational Field Equations
Mathematics Department, Faculty of Science, Minia University, El-Minia, Egypt
Mathematics Department, Faculty of Science, Minia University, El-Minia, Egypt
Higher Institute for Engineering and Technology, El-Minia, Egypt
- 1 Mathematics Department, Faculty of Science, Minia University, El-Minia, Egypt
- 2 Mathematics Department, Faculty of Science, Minia University, El-Minia, Egypt
- 3 Higher Institute for Engineering and Technology, El-Minia, Egypt
Applied Mathematics·Volume 13 (2022)·Pages 1022–1032·Published 28 December 2022·DOI10.4236/am.2022.1312063
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Abstract
The Bach equations are a version of higher-order gravitational field equations, exactly they are of fourth-order. In 4-dimensions the Bach-Einstein gravitational field equations are treated here as a perturbation of Einstein’s gravity. An approximate inversion formula is derived which admits a comparison of the two field theories. An application to these theories is given where the gravitational Lagrangian is expressed linearly in terms of R , R 2 , | Ric | 2 , where the Ricci tensor Ric = R αβ d x α d x β is inserted in some formulas which are of geometrical or physical importance, such as; Raychaudhuri equation and Tolman’s formula.
KeywordsGravitational TheoryHigher Order GravityBuchdahl’s FormulaBach-Einstein Gravitational Field EquationsRaychaudhuri EquationTolman’s Formula
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