General Relativistic Accelerated Motion

Since Newton discovered his laws of motion and gravitation, the understanding of motion, especially acceleration and deceleration, has become crucial. He and his followers extended these ideas to non-inertial frames. A significant advancement was the investigation of motion in Einstein`s Special Relativity, particularly accelerated motions over very short time intervals. A common example is an object moving with constant acceleration. However, to fully grasp dynamics, we need Einstein`s General Relativity (GR), which includes the effects of gravity and how masses curve space. There has been little research so far on accelerated motion in the curved spacetime of GR in general. This project aims to develop a new framework to understand this by examining different spacetime geometries to study motions of matter not aligned with the flow of spacetime. It aims to establish a connection between the Newtonian gravitation and GR to explain specific gravitational effects. Initially, a comprehensive analytical framework for such "tilted" spacetimes will be developed, before specific cases like those considered in `warp-drive` spacetimes are explored in depth. Current studies often neglect the significance of tilted and accelerated motion in these spacetimes, leading to unrealistic models. The goal is to devise a method to address these issues and answer open questions. The project will also investigate cosmological problems such as the flow of large galaxy groups and discrepancies in measurements of the Universe`s expansion rate. The developed models should be flexible enough to capture both large-scale and local cosmic structures, unlike existing models that often focus on a single scale only. Some of these models may also be relevant to theories involving faster-than-light travel. Various ideas will be explored, including a theory that extends Newtonian gravitation to include effects predicted uniquely by GR, such as gravitoelectromagnetism. Motion in cosmological models is often associated with a dipole, thus exact solutions of GR that include a dipole structure like the Szekeres class will be examined. The Lyon team has developed tools for detailed modeling of large- scale structures in both Newtonian and Einsteinian cosmology, which will aid in understanding patterns in the Universe detected by ongoing and forthcoming observational programs of supernovae and highly redshifted galaxies. This project lies at the intersection of various research fields and benefits from combined knowledge in these areas.