A Derivation of the Hubble- Lemaître Law that Identifies Dark Energy and Dark Matter
I apply a generalized FLRW metric in a spherically symmetric coordinate frame. This leads to the discovery that, within this framework, the gravitational field has an equation of state of (EoS) w = −1. In the spacetime defined by the gravitationally perturbed Robertson-Walker metric, the gravitational pressure is found to be negative. A gravitational positive feedback cycle, recognized in Einstein’s seminal work - The Foundation of the Theory of General Relativity - gives rise to the self-induction of gravity that leads to the continuous growth of the field, even in the absence of changes in gravitating bodies. This auto-induced growth of the gravitational field is, here, proposed to manifest as the expansion of physical space - the latter, here, being proposed as the form of the field - attributed to dark energy, and certain unexpected velocity profiles of orbits and extensive regions of gravitational lensing attributed to dark matter. This spatial expansion, by virtue of the natures of the energy conservation laws of gravity and of its EoS, is shown to be locally isobaric. The Hubble-Lemaître law is derived from the isobaric nature of the expansion. This leads to the discovery that the Hubble parameter is a cosmic constant. The Hubble constant references a universal maximum gravitational energy density - H2/2κ ≈ 1.52E-27 Kg m-3 @ H = 2.26E-18 s-1. The expansion, over time, lends a historical character to the laws of gravitation. Continuous expansion of the field and so of its form - space - is essential in preventing their collapse.