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The recent starting of the gravitational wave (GW) astronomy with the eventsGW150914, GW151226, GW170104, and the very recent GW170814 and GW170817 seemsto be fundamental not only in order to obtain new intriguing astrophysicalinformation from our surrounding Universe, but also in order to discriminateamong Einstein's general theory of relativity (GTR) and alternativegravitational theories. At the present time, despite the cited events, and inparticular the last ones, which are the events GW170814 and GW170817, have putvery strong constraint on the GTR, extended theories of gravity have not beencompletely ruled out. Here we discuss, in our knowledge for the first time inthe literature, GWs in the Rastall theory of gravity. In fact, the Rastalltheory recently obtained a renovated interest in the literature. We show thatthere is a profound analogy between GWs in f(R) theories of gravity and GWs inthe Rastall theory. This will permit us to linearize the Rastall fieldequations and to find the corresponding GWs. We will also study the motion ofthe test masses due to GWs in this theory which could help, in principle, todiscriminate between the GTR, f(R) theories and the Rastall theory of gravity.

Third gravitational wave polarization mode in Rastall theory and analogy with f(R) theories