Updated: Mar 21, 2019
The historical evolution of gravitational waves is presented by analogy with geometrical optics and electrodynamics. Whereas to Newton curvature and force are intertwined, general relativity asserts that a gravitational field can exist even in empty space . General relativity is shown to be equivalent to geometrical optics, where particles propagate along geodesics with zero acceleration, thereby limiting the type of cataclysmic phenomena it can describe. Hence, there is not one (non-Euclidean) geometry that can cover the entire field of physical phenomena, making it necessary to analyze sectional curvature in each instance. It is as Newton claimed: force determines the character of the curve and conversely. The assumption that gravitational waves travel at a finite velocity means they should manifest aberration like their electromagnetic counterparts. Since radiation and aberration go hand-in-hand: the spectral density of black radiation goes as the fourth power of the temperature while gravitational radiation varies as the seventh power. There is a physical gap, if not a logical one, between numerical and general relativities. The former relies on a (3 space+1 time) decomposition of the Einstein equations, while the latter has no preferential time-slicing so that there is no unique instantaneous direction. General relativity has not been able to solve the two-body problem, yet numerical relativity claims to describe the inspiraling of compact binaries, whether they be neutron stars or black holes. Yet, the founding fathers of general relativity were unaware of their existence although; nevertheless they are clearly seen to be children of the same parents. Supposedly, this is due to "recent" advances like numerical relativity and post-Newtonian methods, making them something more than the theory they are founded upon, or have any connection to. One may rightly question as to what they are approximations of? Certainly they are not approximations of general relativity or Newtonian dynamics. Other topics include discordant red-shifts of quasars, cosmic strings and black holes, the explanation of flat rotational velocity curves of spiral galaxies by 2 dimensional gravitational lensing, the dimensional distinction between the gravitational bending of light treated by Soldner and then Einstein, the derivation of the perihelion shift as the gravitational analog of Weber's electrodynamic equation making it something more than 'gap' fitting, and the suitability of optical interferometers in the detection of gravitational waves.