2001•Unpublished venueRequires access

The Newtonian limit of fourth and higher order gravity ∗

Ines Qu, Hans‐Jürgen Schmidt

Abstract

We consider the Newtonian limit of the theory based on the Lagrangian ( p∑ L = R + k=0 ak R ✷ k R √−g 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 ( p∑ Φ = m/r 1 + ci exp(−r/li) i=0 with ∑ p i=0 ci = 1/3. Therefore, the potential is always unbounded near the origin. Wir betrachten den Newtonschen Grenzwert der durch den Lagrangian

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Key concepts: Physics, Newtonian potential, Yukawa potential, Newtonian fluid, Limit (mathematics), Newtonian limit, Gravitational potential, Gravitation