Author(s)

Fathy Ibrahim Abdel-Bassier¹, Ahmed Fouad Abdel-Wahab¹, Fayrouz Mostafa Abdel-Maboud²

¹Mathematics Department, Faculty of Science, Minia University, El-Minia, Egypt.
²Higher Institute for Engineering and Technology, El-Minia, Egypt.

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, R², |Ric|², where the Ricci tensor Ric = R_αβdx^αdx^β is inserted in some formulas which are of geometrical or physical importance, such as; Raychaudhuri equation and Tolman’s formula.

Gravitational Theory, Higher Order Gravity, Buchdahl’s Formula, Bach-Einstein Gravitational Field Equations, Raychaudhuri Equation, Tolman’s Formula

Abdel-Bassier, F. , Abdel-Wahab, A. and Abdel-Maboud, F. (2022) Bach-Einstein Gravitational Field Equations as a Perturbation of Einstein Gravitational Field Equations. Applied Mathematics, 13, 1022-1032. doi: 10.4236/am.2022.1312063.