CENTRA Seminar - Gravity in higher dimensions: Pure Lovelock gravity - 19 julho 2018

It is well-known that Einstein gravity is kinematic (no non-trivial vacuum solution, i.e., Riemann vanishes whenever Ricci does so) in 3 dimension because Riemann is entirely given in terms of Ricci. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in action) gravity for which Nth order Lovelock Riemann tensor is indeed given in terms of corresponding Ricci for all odd  d=2N+1 dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good discerning and guiding criterion for gravitational equation in higher dimensions.