2017/08/31 by Marcello Ortaggio
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Base (topology) #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Coupling (piping) #Degenerate energy levels #Field (mathematics) #Geometry #Killing vector field #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Null (SQL) #Null vector #Physics #Pure mathematics #Quantum mechanics #Riemann hypothesis #Space (punctuation) #Type (biology) #Vector field #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.97.044051
published as Phys. Rev. D 97, 044051 (2018) · 20 pages. v2: new section 7 (base space as a direct product), a few comments added, new refs
openalex publication_date 2018/02/28 · arxiv created 2018/03/07 · arxiv updated 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Vacuum solutions of Lovelock gravity in the presence of a recurrent null vector field (a subset of Kundt spacetimes) are studied. We first discuss the general field equations, which constrain both the base space and the profile functions. While choosing a ``generic'' base space puts stronger constraints on the profile, in special cases there also exist solutions containing arbitrary functions (at least for certain values of the coupling constants). These and other properties (such as the pp- waves subclass and the overlap with VSI, CSI and universal spacetimes) are subsequently analyzed in more detail in lower dimensions n=5, 6 as well as for particular choices of the base manifold. The obtained solutions describe various classes of nonexpanding gravitational waves propagating, e.g., in Nariai-like backgrounds M2\ifmmode×\else\texttimes\fi\mathrm\ensuremathΣ_n\ensuremath-2. An Appendix contains some results about general (i.e., not necessarily Kundt) Lovelock vacua of Riemann type III/N and of Weyl and traceless-Ricci type III/N. For example, it is pointed out that for theories admitting a triply degenerate maximally symmetric vacuum, all the (reduced) field equations are satisfied identically, giving rise to large classes of exact solutions.