S\'aez-Ballester and Einstein-massless-scalar systems are one and the same theory!

Abstract

In this paper we demonstrate that S\'aez-Ballester theory (SBT) is not a scalar-tensor theory (STT) of gravity as widely acknowledged. Moreover, SBT is identified with the (minimally coupled) Einstein-massless-scalar (EMS) theory. We discuss on several known solutions of SBT and we show that these are also solutions of the EMS system and viceversa. Cosmological arguments are also considered.Comment: 6 pages, no figures. The longstanding misconception on the (incorrect) classification of S\'aez-Ballester theory as a scalar-tensor theory is amended. Bibliographic references added and acknowledgements modifie