Einstein‘s Geometrization vs. Holonomic Cancellation of Gravity via Spatial Coordinate-rescale and Nonholonomic Cancellation via Spacetime Boom

Particle‘s acceleration in static homogeneous gravitational field is cancelled by any reference frame of the same accelerating direction and the same accelerating rate. The frame is commonly called the freely-falling one. The present paper shows that the acceleration is also cancelled by a spatial curvilinear coordinate system. The coordinate system is simply a spatial square-root coordinate rescale in the field direction, no relative motion being involved. This suggests a new equivalence principle. Spacetime is flat which has inertial frame of Minkowski metric ηij . Gravity is a tensor gαβ on the spacetime, which is called effective metric. The effective metric emerges from the coordinate transformation. The gravitational field of an isolated point mass requires a nonholonomic spacetime boom transformation. This generalization of Newtonian gravity shares the aesthetic properties of Lorentz transformation, which should help quantize gravity. The corresponding effective metric is different from that of Schwarzschild. To first order, its prediction on the deflection of light and the precession of the perihelia of planetary orbits is the same as the one of general relativity (GR). However, the metric has the important prediction that the common angular momentum is not conserved. Instead, the shadow angular momentum is conserved. Because the distance between a point and its shadow is GM/c2 (≈ 1.5km for the mass of sun), the test on the prediction needs high precision solar or other observations and is left for future work. keywords: Relativity – Gravitational Theory – Galaxies : Structure