Gravitational Radiation and Black Holes in Thomas-Whitehead (TW) Gravity

Tyler Grover; University of Iowa

The coadjoint orbit action of the Kac-Moody and Virasoro semi-direct product algebra obtains the WZNW action and a modified Polyakov action incorporating a field D, the diffeomorphism field. The pure Kac- Moody coadjoint element corresponds to the Yang-Mills gauge potential in higher dimensions and the pure Virasoro coadjoint element corresponds to the diffeomorphism field, a component of the Thomas-Whitehead connection (The connection on a volume bundle of the projective equivalence class of affine connections for a manifold M.) The diffeomorphism field is understood as a component of the connection describing projective geometry. TW gravity incorporates projective and metric geometry as a theory of gravitation.

To start with, I'll present the action and field equations for TW Gravity. Then, I'll show in a weak field limit, the diffeomorphism field supports transverse-traceless, longitudinal, and scalar modes. These modes are being investigated as a source for geodesic deviation. By incorporating a cosmological constant in the action, I'll also show that TW Gravity admits Ds/Ads spacetime solutions (notably dS/AdS black hole solutions).