Nordstrom's scalar theory of gravity and the equivalence principle

TL;DR

Nordstrom's scalar gravity theory, while observationally invalid, uniquely satisfies the strong equivalence principle among gravity theories with General Relativity, a property linked to a special superpotential.

Contribution

The paper demonstrates that Nordstrom's theory obeys the strong equivalence principle beyond post-Newtonian approximation, revealing a fundamental connection to a 'Nordstrom-Katz' superpotential.

Findings

Nordstrom's theory obeys the strong equivalence principle beyond post-Newtonian level

The property is related to the existence of a 'Nordstrom-Katz' superpotential

The theory is observationally ruled out but theoretically significant

Abstract

Nordstrom's theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a 'Nordstrom-Katz' superpotential.