Total Gravitational Force Re-cast in Complex Space-Time Frame

Abstract

Einstein’s general theory of relativity provoked the need to have an experiment if it had to be considered valid. As a result, Gravity Probe-B experiment was suggested and conducted. The results of the GP-B experiment have shown that the general theory of relativity was correct but it is limited. More information was revealed from this experiment than the earlier predictions. Several theoretical researches have been attempted to develop a single model that puts together the predictions or GR and the experimental result. This has not happened. A major setback in the numerous studies towards obtaining such a model has been the lack of a robust and well elaborate mathematical structure. This study has therefore identified a comprehensive mathematical structure to re-cast the predictions and also determine the finer details of the extra experimental data with accuracy. The new mathematical structure re-defines the four vector frame by expressing the fourth time axis as a vector just like the three well known spatial axes. However, the time axis is assumed to take a general orientation as opposed to the spatial axes which are mutually orthogonal. The unit vector on the time axis is complex and it is represented by the temporal unit vector . The four-vector mathematics in this complex plane agrees with the three-dimensional vector mathematics that is well established. This study therefore intends to comprehensively reformulate geodetic effect and frame-dragging effect.