2020/03/31 by H. Lü, H. Lu, Yi Pang · 3 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Einstein #Gauss–Bonnet gravity #Gauss–Bonnet theorem #Geometry #Gravitation #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar curvature #Scalar field #Space (punctuation) #Theoretical physics #f(R) gravity #gr-qc #hep-th
paper · pdf · doi:10.1016/j.physletb.2020.135717
published as Phys.Lett.B809 (2020) 135717 · Latex, 11 pages, published version
openalex created_date 2020/04/03 · arxiv created 2020/08/25 · openalex publication_date 2020/08/25 · arxiv updated 2020/09/03 · openalex updated_date 2026/08/05
We propose a procedure for the D→4 limit of Einstein-Gauss-Bonnet (EGB) gravity that leads to a well defined action principle in four dimensions. Our construction is based on compactifying D-dimensional EGB gravity on a (D−4)-dimensional maximally symmetric space followed by redefining the Gauss-Bonnet coupling α→αD−4. The resulting model is a special scalar-tensor theory that belongs to the family of Horndeski gravity. Static black hole solutions in the scalar-tensor theory are investigated. Interestingly, the metric profile is independent of the curvature of the internal space and coincides with the D→4 limit of the usual EGB black hole with the unusual Gauss-Bonnet coupling αD−4. The curvature information of the internal space is instead encoded in the profile of the extra scalar field. Our procedure can also be generalized to define further limits of the Gauss-Bonnet combination by compactifying the D-dimensional theory on a (D−p)-dimensional maximally symmetric space with p≤3. These lead to different D→4 limits of EGB gravity as well as its D→2,3 limits.