Reviewing the Mathematical Physics of General Relativity: Is Contraction of Radial Space from the Gravitational Radius as Valid a Solution as Radial Curvature?

In the Système Internationale (SI) of units, time is now defined by the microwave frequency of a hyperfine transition for the caesium 133 atom, also giving a measure for space by its wavelength, since the local light speed is selected to equal their product (c=λv). Einstein’s principle of relativistic physics demands that the speed of light (c) determined in all reference frames be found equal. Yet asymmetries of space and time result if local measures of frequency and wavelength for one radial reference frame for gravity are used for observations made of another. His highly predictive time-dilating general relativity lengthening radial separation required gravitational curving of space in a non-Euclidean Riemann manifold. This prediction is amply confirmed by observations. Yet it lacks a convincing physical cause. By contrast, in radial relativity internal voids of elementary particles are assumed to shorten radial separation between material bodies by gravitational radii (Σro) in a Euclidean framework. This assumption yields rational algorithms for covariant relativity that reduce clock frequencies and extend radial space for observations made of processes closer to a gravitational centre of mass (M). Dilating time by reduced frequency [ν(1–ro/r)] and extending wavelength as the measure of space [(λ/(1– ro/r)] equally preserves the speed of light (c = νλ) when compared to all other viewpoints towards infinity. A transverse scale for least action frequency [ν(1 – V2/2c2)] varying with radial curvature (1/r) also dilates time, as shown in the Lorentzian transform for special relativity. Our radial action algorithms set gravitational fields and radial curvatures at infinity equal to zero and shorten central space to a surface at r0 of maximum radial curvature, with no central singularity required. Every gravitational environment naturally selects its own clock speed and wavelength minimizing all actions including biological processes. These radial action algorithms are tested and their equivalence shown for all aspects of general relativity as Lagrangian variations.