Black holes in Thomas-Whitehead projective gravity

Einstein’s theory of General Relativity describes gravitation and its feature through the curvature of spacetime where objects in free fall are just following their geodetic specified by their initial data. The observed dynamics in spacetime should be invariant of choice of parameterization. We can ask then “What connections are equivalent in that they cast the same geodesics as unparameterized curves?” The answer is “Those which are related by a projective transformation.” Thomas Whitehead projective gravity is a theory of gravity that describes gravitation in the context of projectively equivalent connections. Two independent field arise in the Thomas Whitehead projective connection, the fundamental projective invariant Π and the Diffeomorphism field ꓓ. The Diffeomorphism field appearing in the connection is the higher dimensional analog of the Diffeomorphism field appearing in one dimension arising from the coadjoint orbits of the Virasoro algebra in string theory.

Here we propose a project to investigate gravitational sources in the context of this theory, and the potential for features of TW projective gravity to explain the mysteries of what sources black holes, The dark matter halos as a contribution from the energy momentum tensor for the fields Π and D sourced by the supermassive black hole at the center of galaxies.