Evolution of Lovelock Tensor as a Generalized Einstein Tensor and Lovelock Gravity under Ricci Flow

The higher dimensional gravity theory of Lovelock is a fascinating generalization of Einstein’s gravity theory and it is of extreme interest in theoretical physics as it delineates a wide class of relativistic models. Here, we propose a short digest on Lovelock theory that represents a very beautiful scenario to study how the differential geometry of gravity results corrected at short distance due to the presence of higher order curvature terms in the action. As in the modern literature of cosmology, the space-time has been supposed to be a dynamical manifold. Hence by admitting this fact in the present study, we will be concerned with the flow equations of all the Lovelock configurations. In particular, we shall make use of Ricci flow techniques to evolve the actions which are responsible for higher order gravity theory. Finally, we shall attempt to evolve the Lovelock tensor to generate a very useful non-linear heat diffusion equation that could analyze the mystery of higher order gravity theory.