On the Gauss-Bonnet Gravity

Abstract

We argue that propagation of gravitational field in the extra dimension is motivated by physical realization of second iteration of self interaction of gravity and it is described by the Gauss-Bonnet term. The most remarkable feature of the Gauss-Bonnet gravity is that at high energy it radically transforms radial dependence from inverse to proportionality as singularity is approached and thereby making it weak. Similar change over also occurs in approach to singularity in loop quantum gravity. It is analogous to Planck's law of radiation where similar change occurs for high and low energy behavior. This is how it seems to anticipate in qualitative terms and in the right sense the quantum gravity effect in 5 dimensions where it is physically non-trivial. The really interesting question is, could this desirable feature be brought down to the $4-$dimensional spacetime by dilatonic coupling to the Gauss-Bonnet term or otherwise?