2015/06/16 by Naresh Dadhich · 44 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Einstein #Einstein tensor #Einstein's constant #Exact solutions in general relativity #Geometry #Gravitation #Lanczos tensor #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Ricci curvature #Ricci decomposition #Ricci flow #Riemann curvature tensor #Tensor (intrinsic definition) #Theoretical physics #Weyl tensor #gr-qc #hep-th
paper · pdf · doi:10.1140/epjc/s10052-016-3933-z
published in The European Physical Journal C 76(3) (Springer Science+Business Media)
arxiv created 2015/06/16 · openalex publication_date 2016/02/26 · openalex created_date 2016/06/24 · arxiv updated 2017/10/19 · openalex updated_date 2026/08/05
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, 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 distinguishing and guiding criterion for the gravitational equation in higher dimensions.