Theoretical corrections on scalar gravitational waves

Following some ideas in the Landau’s book, some corrections about errors in the old literature on scalar gravitational waves are given and discussed. Even if such errors can be considered not important from the point of view of observations, because they do not alter the interferometric response function for scalar gravitational waves, the presented analysis is due and very important for a sake of completeness and for a better understanding of the linearized theory of Scalar-Tensor Gravity. Recently, the data analysis of interferometric gravitational waves (GWs) detectors has been started (for the current status of GWs interferometers see [1]) and the scientific community aims in a first direct detection of GWs in next years. Detectors for GWs will be important for a better knowledge of the Universe and either to confirm or rule out the physical consistency of General Relativity or of any other theory of gravitation (see [2] for a review). In fact, in the context of Extended Theories of Gravity, some differences between General Relativity and the others theories can be pointed out starting by the linearized theory of gravity. In this picture, detectors for GWs are in principle sensitive also to a hypothetical scalar component of gravitational radiation that appears in scalar-tensor gravity [3]. With the aid of some ideas in the Landau’s book, in this letter we show some corrections about errors in the old literature on scalar GWs (SGWs). Fortunately, it will result that we can neglect such errors from the point of view of observations, because they only change a sign in the interferometric response function for SGWs. However, we think that the presented analysis is due and quite important for a sake of completeness and for a better understanding of the linearized theory of Scalar-Tensor Gravity. Let us start from the work [4], which was improved from the work [5]. In [4], the authors did not realize that in their gauge the beam splitter is not left at the origin by the passage of the SGW, and furthermore computed a coordinatetime interval than a proper-time interval, reaching the incorrect conclusion that