Assessment of Variable Speed of Light with Time and General Relativity

Background: In a previous paper entitled: "Evidence for the variation of the speed of light over time" [1], a series of observational evidences was presented in favor of the hypothesis that the speed of light varies over time according to the fundamental relationship dc / dt = - Hc, where H is the Hubble constant which is considered a universal constant.

Objectives: In this paper we aim to summarize and reinforce the observational evidences in support of the hypothesis and to probe the consequences of this relationship on General Relativity.

The hypothesis of c variable with time provides a different interpretation of the nature of the cosmological redshift, and the Hubble constant is not understood as the rate of expansion of the universe with time, but as the rate of decrease of c with time.

Methods: We will show how this relationship provides a clear explanation for the phenomenon of the so-called "anomalous acceleration" suffered by all spacecraft after leaving the solar system [2].

We will provide a theoretical justification of the fundamental relationship and show how the theoretical trend of the galactic velocity curves can be deduced from it.

We will therefore give a theoretical foundation to the constant a0 introduced by the MOND theory to successfully explain the galactic velocity curves on the basis of baryon matter alone [3].

Results: The important Tully-Fisher empirical relationship that connects the galactic velocity curves to the baryon mass of the galaxy [4,5] is theoretically deduced and the apparent (accelerated) expansion of the universe is justified without intervening elusive entities such as dark matter and dark energy.

Conclusion: It is concluded that the link between the variation of c over time and the variation of other important physical constants is explored, showing how this leads to an unexpected link between the electromagnetic phenomena, represented by c, and the gravitational ones, represented by G.