2011/03/31 by Benjamin Ett, David Kastor
Physics and Astronomy · #Ansatz #Black Holes and Theoretical Physics #Constant curvature #Cosmological constant #Cosmology and Gravitation Theories #Curvature #Degenerate energy levels #Einstein #Gauge theory #Pulsars and Gravitational Waves Research #Vacuum state #f(R) gravity #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep04(2011)109
published as JHEP 1104:109,2011 · 14 pages; v2 reference added
arxiv created 2011/04/01 · openalex publication_date 2011/04/01 · arxiv updated 2011/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze the field equations of Lovelock gravity for the Kerr-Schild metric ansatz, gab= gab +λkakb, with background metric gab, background null vector ka and free parameter λ. Focusing initially on the Gauss-Bonnet case, we find a simple extension of the Einstein gravity results only in theories having a unique constant curvature vacuum. The field equations then reduce to a single equation at order λ2. More general Gauss-Bonnet theories having two distinct vacua yield a pair of equations, at orders λ and λ2 that are not obviously compatible. Our results for higher order Lovelock theories are less complete, but lead us to expect a similar conclusion. Namely, the field equations for Kerr-Schild metrics will reduce to a single equation of order λp for unique vacuum theories of order p in the curvature, while non-unique vacuum theories give rise to a set of potentially incompatible equations at orders λn with 1≤ n ≤ p. An examination of known static black hole solutions also supports this conclusion.