The Physics Society of Iran Iranian Journal of Physics Research 1682-6957 5 3 2019 11 26 A class of exact solutions of higher derivative gravity in four dimensions A class of exact solutions of higher derivative gravity in four dimensions 153 156 675 FA M. H. Dehghani H. Mohammad Pour Journal Article 2019 11 26  In this paper we consider the action of higher derivative gravity up to the second order terms in the scalars made from the Ricci scalar, Ricci and Riemann tensors. We use the Bach- Lanczos identity of the Weyl tensor in four dimensions and show that the solutions of 4-dimensional Einstein equations with cosmological constant term in vacuum, which are known as Einstein metrics, satisfy the field equations of higher derivative gravity. We also find that the field equations of higher derivative gravity are not satisfied by the solutions of Einstein equations in higher dimensions or in the presence of matter.  In this paper we consider the action of higher derivative gravity up to the second order terms in the scalars made from the Ricci scalar, Ricci and Riemann tensors. We use the Bach- Lanczos identity of the Weyl tensor in four dimensions and show that the solutions of 4-dimensional Einstein equations with cosmological constant term in vacuum, which are known as Einstein metrics, satisfy the field equations of higher derivative gravity. We also find that the field equations of higher derivative gravity are not satisfied by the solutions of Einstein equations in higher dimensions or in the presence of matter. https://ijpr.iut.ac.ir/article_675_8fecb20817b3847419bb3de39a609afe.pdf