Solar System test for the existence of gravitational waves

Starting from a static spherically symmetric solution of the Einstein’s field equations in the second approximation in the perfect fluid scheme, in the exterior of the source, the corresponding metrics depend on a dimensionless parameter $\alpha$ . Taking the Sun for the source, the influence of $\alpha$ on the classical Solar System tests of the general relativity is estimated, the only $\alpha$-dependent one being the Shapiro radar-echo delay experiment. Performing such a test in given conditions within a precision better than ${10}^{-2}$, it is possible to obtain an experimental value for $\alpha$ . If $\alpha =1$, the Einstein’s equations in the weak field approximation take the D’Alembert form, which attests the existence of gravitational waves