The Newtonian limit of fourth and higher order gravity

Abstract

Abstract We consider the Newtonian limit of the theory based on the Lagrangian \documentclass{article}\pagestyle{empty}\begin{document}$ \ell = (R + \sum\limits_{k = 0}^p {a_k R\square ^k R)\sqrt { - g.} } $\end{document} . The gravitational potential of a point mass turns out to be a combination of Newtonian and Yukawa terms. For sixth‐order gravity ( p = 1) the coefficients are calculated explicitly. For general p one gets \documentclass{article}\pagestyle{empty}\begin{document}$ \phi = m/r(1 + \sum\limits_{t = 0}^p {c_i } \exp (‐ r/l_i))\;with\;\sum\limits_{t = 0}^p {c_i} \; = \;1/3 $\end{document} . Therefore, the potential is always unbounded near. The origin.