https://doi.org/10.1140/epjc/s10052-016-3933-z
Regular Article - Theoretical Physics
A distinguishing gravitational property for gravitational equation in higher dimensions
1
Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, 110025, India
2
Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Pune, 411 007, India
* e-mail: nkd@iucaa.in
Received:
19
October
2015
Accepted:
4
February
2016
Published online:
26
February
2016
It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. 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 the action) gravity for which the Nth order Lovelock–Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, 
, 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 distinguishing and guiding criterion for the gravitational equation in higher dimensions.
© The Author(s), 2016
