Kundt spacetimes in the Einstein-Gauss-Bonnet theory

Abstract

We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any dimension. The field equations are explicitly derived and simplified, and their solutions classified into three distinct subfamilies. Algebraic structures of the Weyl and Ricci curvature tensors are determined. The corresponding curvature scalars directly enter the invariant form of equation of geodesic deviation, enabling us to understand the specific local physical properties of the gravitational field constrained by the EGB theory. We also present and analyze several interesting explicit classes of such vacuum solutions, namely the Ricci type III spacetimes, all geometries with constant-curvature transverse space, and the whole pp-wave class admitting a covariantly constant null vector field. These exact Kundt EGB gravitational waves exhibit new features which are not possible in Einstein's general relativity.

arXiv comment22 pages, to appear in Phys. Rev. D

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Cited by in corpus (8)

• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter
• Kundt geometries and memory effects in the Brans-Dicke theory of gravity
• Kundt Three Dimensional Left Invariant Spacetimes
• Kundt wave geometries in Eddington-inspired Born-Infeld gravity: New solutions and memory effects
• Anisotropy in constraint 4D Gauss-Bonnet gravity
• Kundt Gravitational Waves Coupled with a Non-Noetherian Conformal Scalar Field
• Analyzes of Algebraic Classification of Higher Dimensional Kundt Geometries with Large $D$ Method