2015/05/31 by Sourya Ray · 3 citations
Mathematics · Physics and Astronomy · #Algebraic number #Base (topology) #Black Holes and Theoretical Physics #Field (mathematics) #Function (biology) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Metric (unit) #Noncommutative and Quantum Gravity Theories #Product (mathematics) #Space (punctuation) #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/32/19/195022
published as Class. Quantum Grav. 32 (2015) 195022 · minor corrections, matches the published version
openalex publication_date 2015/09/17 · arxiv created 2015/09/18 · arxiv updated 2015/09/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We extend the Birkhoff's theorem in Lovelock gravity for arbitrary base manifolds using an elementary method. In particular, it is shown that any solution of the form of a warped product of a two-dimensional transverse space and an arbitrary base manifold must be static. Moreover, the field equations restrict the base manifold such that all the non-trivial intrinsic Lovelock tensors of the base manifold are constants, which can be chosen arbitrarily, and the metric in the transverse space is determined by a single function of a spacelike coordinate which satisfies an algebraic equation involving the constants characterizing the base manifold along with the coupling constants.