Haar Wavelets and the Origin of Gravitational Inertia

Abstract

Spacetime is considered to be everywhere Minkowski except at the location where a signal wave of energy interacts with the gravitational field. The conformal metric f[k(x-vt)]Nuv is suitably chosen to represent this interaction, where f[k(x-vt)]is a generalized wave or signal function. Parametrized and Taylor expanded at zero, the spacetime metric is transformed into a Haar wavelet having parameter width tau. Applying the Haar metric to the time component of General Relativistic wave equation reduces it from a second ordered covariant differential equation to a first ordered partial differential equation that allows the Einstein Tensor to be easily be expressed in the familiar Poisson form for gravitation. By comparison with the matter density of this equation, to the Haar-Einstein result, shows that the wavelength of a graviton becomes the fundamental source for gravitational attraction. Since the signal wave is unidirectional, it strongly supports Machs assumption that inertia arises from all the matter in the universe. Furthermore, because the Haar metric is conformal, the signal metric is solved for exactly.