Brief Review of Lorentz-Covariant Scalar Theories of Gravitation

An historical review of Lorentz-covariant scalar theories of gravitation is presented. Included are the theory of Poincaré, its presentation by Kottler, and its modification by Whitrow and Morduch; the first theory of Nordström, its modified form due to Bergmann, the modifications due to Whitrow and Morduch, and the field-theoretic approach of Thirring; the second theory of Nordström; and the theory of Kustaanheimo. The extent to which these theories can be said to be in accord with the experimental evidence concerning red shift, advance of the perihelion of Mercury, and deflection of light rays is discussed. It is found that except for red shift, there is, at best, poor agreement and, at worst, disagreement.