Math Physics Seminar
The Thomas-Whitehead projective gravity theory has its origins in string theory. The identified correspondence between the of the coadjoint elements of the Virasoro algebra and Sturm-Liouville operators. This identification of the projective structure in one dimension allows for relating the Virasoro algebra and projective geometry in higher dimensions. We've examined how the Thomas Whitehead projective connection can be used to form a projective curvature tensor, that is then used to build an action for Thomas Whitehead projective gravity. The fields Pi and D of the Thomas-Whitehead connection can provide a source for gravitation through an associated energy momentum tensor. We consider the Pi and Diffeomorphism fields as providing a source for the supermassive black hole. We propose to investigate this possibility the energy momentum tensor contributions from the emanated Pi and D fields corresponding to supermassive black hole solutions could supply the dark matter contribution to galaxy rotation curves. The projective geodesic deviation equation result allows for us to identify the possibility of gravitational radiation independent of the metric degrees of freedom. We would like to explore these features to make predictions about the possible gravitational radiation or tidal effects from Black Holes in Thomas-Whitehead gravity. In this talk, I'll review the background for this work, and discuss what progress has been made with this investigation.