Dynamical Projective Curvature in Gravitation

TL;DR

This paper introduces a novel approach using projective connections and curvature invariants to describe gravitational interactions and dynamics, potentially extending to higher-dimensional theories.

Contribution

It demonstrates how projective Ricci tensors naturally emerge in 2D gravity and proposes an action based on Thomas-Whitehead invariants for dynamic projective connections.

Findings

Metric interaction arises from projective Ricci tensor in 2D gravity

Defined an action for projective connection dynamics using curvature invariants

Discussed implications for higher-dimensional gravitation theories

Abstract

By using a projective connection over the space of two-dimensional affine connections, we are able to show that the metric interaction of Polyakov 2D gravity with a coadjoint element arises naturally through the projective Ricci tensor. Through the curvature invariants of Thomas-Whitehead, we are able to define an action that could describe dynamics to the projective connection. We discuss implications of the projective connection in higher dimensions as related to gravitation.