In this article, we will demonstrate, based upon strictly logical reasoning and cosmic observations results, how gravitational time dilation exerts influences upon light propagation speed and upon gravity propagation speed.Neutron stars mergers have shown that the speed of gravity coincides with the speed of light. However, according to general relativity, time dilates extremely near a black hole. For example, when a photon approaches a black hole, according to observes on the earth, the time will slow down and eventually stop, so, according to observes on the earth, the photon would move extremely slowly towards the black hole so that it will take forever for the photon to enter into the black hole. So, the matter and energy inside a black hole will never interact with photons generated by other celestial bodies, according to observers on the earth. This indicates that gravitational time dilation has effect on light propagation. But, in contrast, gravitational time dilation should have no effect on the propagation of gravity, because the matter and energy inside a black hole obviously can interact with gravitational fields generated by other celestial bodies, according to observers on the earth. This can be shown by such a thought experiment: according to E=mc2, it is possible to transfer an enormous amount of energy to a place near a black hole and create some matter(some particles or even a star) there with these energy. Once created, the matter will start to generate both gravity field and electromagnetic field(light) and the gravity field and electromagnetic field will propagate in each direction, and the light it generates will NEVER enter into the black hole so its electromagnetic fields will never interact with the black hole, according to observers on the earth. But, according to observes on the earth, will the gravity field it generates ever enter into the black hole and interact with the black hole? According to our current mainstream science, the gravity field it generates will quickly enter into the black hole and interact gravitationally with the black hole, according to observers on the earth. Thus, if gravitational time dilation theory is correct, near a black hole, gravity speed is faster than light speed. Although in zero gravity, gravity speed coincides with light speed.

Gravitational waves and lensing of the metric theory proposed by Sobouti We investigate in detail two physical properties of the metric f(R) theory developed by Sobouti (2007). We first look for the possibility of producing gravitational waves that travel at the speed of light. We then check the possibility of producing extra bending in the lenses produced by the theory. We do this by using standard weak field approximations to the gravitational field equations that appear in Sobouti's theory. We show in this article that the metric theory of gravitation proposed by Sobouti (2007) predicts the existence of gravitational waves travelling at the speed of light in vacuum. In fact, this is proved in general terms for all metric theories of gravity which can be expressed as powers of Ricci's scalar. We also show that an extra additional lensing as compared to the one predicted by standard general relativity is produced. These two points are generally considered to be of crucial importance in the development of relativistic theories of gravity that could provide an alternative description to the dark matter paradigm.