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This paper reports a detailed analysis of one of general relativity?s predictions, which claims that light should be deflected by solar gravity. The experimental data related to that prediction are analyzed. The substitution of the direct experimental test for the deflection of visible light during solar eclipses by the indirect measurement of the delay of radio signals traveling between a space probe or from extra galactic sources and the Earth is examined. Three different causes of the delay in the transmission of light near the Sun are examined. They are the relativistic delay, the delay caused by the plasma surrounding the Sun or for a geometric reason. The delay predicted by general relativity is equivalent to a reduced velocity of light in vacuum, in the Sun?s gravitational potential. Since the value of c is defined on Earth, inside the solar gravitational potential, this leads to a double value for the velocity of light on Earth. Furthermore, Einstein?s general relativity predicts that photons slow down when approaching the Sun, so that their velocity must be reduced to zero when reaching the surface of a black hole. This paper shows how all the experiments claiming the deflection of light by the Sun are subjected to very large systematic errors, which render the results highly unreliable. Furthermore, the internal incoherence of general relativity, which leads to a double velocity of light on Earth, adds to the weakness of these tests. Following those difficulties, and since it has also been demonstrated that the deflection of light by a gravitational potential is not compatible with the principle of mass-energy conservation, we show that no one can seriously claim that light is really deflected by the Sun.