The Newtonian Limit in a Family of Metric Affine Theory of Gravitation

D. BARRACO ,VICTOR HAMITY AND ROBERTO GUIBERT

GENERAL RELATIVITY AND GRAVITATION

Año: 1996 vol. 28 p. 339 - 345

0001-7701

{\bf--------------------------------------------------------------------------------------- }\\\noi A brief review of a first order theory with a quadraticLagrangian \linebreak $L = R + w_o R^2$ is presented.  It is shownthat a test particle follows a geodesic of the metric connection. The theory behaves in the Newtonian limit as the Newtonian theory  with a correction which is proportional to the matter density at the   field point.  This behavior can be produced by a Yukawa potential    with an atomic scale characteristic range $\lambda$ and a coupling constant $\alpha$  proportional to $ 1 / \lambda^2$.  This type of potential is not excluded by the present experimental data. } \ {\bf