Gravitation Slows Light and Contracts Yardsticks, Ensuring Invariant Light Speed for All Local Observers

<div xmlns="http://www.tei-c.org/ns/1.0"> The title, of this paper, encapsulates a central conclusion emerging from the reformulation of General Relativity using Deformed Space Geometry in place of the standard Riemannian Geometry framework. This reformulation enables the explanations of some gravitational effects by local variations in the speed of light and yardstick contraction, while preserving the invariance of light speed for all local observers. In General Relativity (GR), local observers consistently measure the speed of light as the invariant constant c, regardless of their position within a gravitational field. However, observers at a radial distance r from a gravitating mass m, perceive the coordinate speed of light as c(r) = (1-2Gm / rc 2 ) c = ac. Traditionally, this coordinate-dependent speed is considered a mathematical artifact without physical significance. It is the change in time with the radial distance that is considered a real effect that explains astrophysical phenomena. We however, consider time as merely a practical term, whereas distance and velocity are fundamental. Thus, we are proposing that c(r) is real while the locally measured invariant c results from gravitational effects on measuring instruments. This perspective is developed within the framework of Deformed Spaces Geometry, an alternative to Riemannian geometry, which retains the formalism and solutions of GR but offers a more intuitive understanding of gravitational phenomena. Our approach addresses longstanding issues in GR and predicts novel phenomena, some of which have been observed in recent experiments conducted at the Hebrew University of Jerusalem. </div>