| dc.description.abstract | Einstein's general theory of relativity governs dynamics in a gravitational field. Linearization of the non-linear field equations converts them to solvable forms. The clear similarity between linearized equations and Maxwell's equations in electrodynamics prompts inference that the gravitational field is inherently composed of electric and magnetic forces as constituent elements. Notably, the electric force component aligns seamlessly with the well-known Newtonian gravity force, while the magnetic force component manifests dynamic phenomena, including the predicted geodetic and frame-dragging effects. A significant constraint emerges in the use of the four-dimensional Minkowski spacetime frame for the derivation and exploration of field equations. This frame, unfortunately, lacks a fully defined unit vector in the temporal direction, thereby impeding essential mathematical operations such as the curl and cross product of vectors that intricately describe dynamic properties. In an endeavour to surmount this impediment, a ground breaking approach is introduced: A novel four-dimensional complex spacetime frame. This frame extends the conventional three-dimensional Euclidean space by incorporating an imaginary temporal axis defined by a unit vector. It has rigorously shown that this innovative approach solves the previously encountered limitations in Minkowski spacetime, facilitating the execution of mathematical operations including curl and cross-product of vectors in a more standard manner. This work presents a comprehensive reformulation of the relativistic gravitational field theory within the novel complex spacetime frame. The resulting field equations are deployed through re-examination of some relativistic effects namely geodetic and frame-dragging effects, with a distinct emphasis on achieving an elevated degree of precision and accuracy in predicting relativistic properties. The end result of this scholarly endeavour is to discern comparative analysis of the obtained results vis-à-vis the empirical findings derived from the Gravity Probe-B experiment. A gravitoelectromagnetic (GEM) field potential four-vector and field strength tensor defined within Minkowski spacetime was calculated and their applications to gyroscope dynamics were discussed leading to a gyromagnetic ratio η=4. A gravitational field strength in a complex spacetime frame was obtained. Electric and magnetic forces in a complex spacetime frame were obtained. expressions for frame-dragging and geodetic effects were obtained. A comparison between obtained results, the results of the GP-B experiment and earlier theoretical result was done. Gyroscope dynamics were found to be characterised by frame-dragging (Lense-Thirring) and geodetic effects. The frame-dragging effect was found to be -2B ⃗_g×q ̂×S ⃗ and that of geodetic effect was found to -3/2 v ⃗/c×E ⃗_g×q ̂×S ⃗ . The directions of the relativistic effects are specified. Comparing with established theoretical findings, it was noted that the magnitude of geodetic effect was exactly equal to that obtained earlier theoretically and experimentally but the numerical value of frame-dragging effect was much smaller. As opposed to earlier results, our findings include the directional components of the relativistic effects providing additional information. A re-evaluation of other physical theories is suggested in future research. | en_US |
