Kundt Gravitational Waves Coupled with a Non-Noetherian Conformal Scalar Field
Pedro A. Sánchez
备注：
14 pages + Refs., 3 figures; To appear in PRD; Added: Kundt waves classes diagram, eq. (50), references, and other minor changes to match journal version
Type N spacetimes of the Kundt class are presented as solutions to Einstein's equations sourced by a real scalar field whose equation of motion is conformally invariant and that generalizes the standard conformal scalar field. The specific spacetimes considered model gravitational waves with uniform and totally geodesic wave fronts, propagating in a maximally symmetric background, and are characterized by the value of their constant scalar curvature and by the so-called wave profile function. All subclasses of such spacetimes are analyzed. It is shown that the scalar field solutions generically divide into two branches, of which one has a strikingly different behavior from that of the standard conformal case. The scalar field contributes to the equation satisfied by the wave profile function by adding new singular terms. Closed form and mode solutions for the wave profile function are found for different scenarios. The resulting energy-momentum tensor has a null eigenvector, but is more general than the pure radiation type usually coupled with this kind of spacetimes.
A particular yet large class of non-diverging solutions which admits a cosmological constant, electromagnetic field, pure radiation and/or general non-null matter component is explicitly presented. These spacetimes represent exact gravitational waves of arbitrary profiles which propagate in background universes such as Minkowski, conformally flat (anti-)de Sitter, Edgar-Ludwig, Bertotti-Robinson, and type D (anti-)Nariai or Plebanski-Hacyan spaces, and their generalizations. All possibilities are discussed and are interpreted using a unifying simple metric form. Sandwich and impulsive waves pr…
Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the sear…
We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some interesting global properties of the spacetimes, such as an inherent rotation of the wave-propagation direction, or the character of singularities. In particular, we demonstrate that the characteristic envelope singularity of the rotated wave-fronts is a (non-scalar) curvature singularity, although all scalar invariants of the Riemann tensor vanish there.
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We study almost universal spacetimes - spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal. Explicit examples of Weyl type II almost universal Kundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories…
We describe a class of impulsive gravitational waves which propagate either in a de Sitter or an anti-de Sitter background. They are conformal to impulsive waves of Kundt's class. In a background with positive cosmological constant they are spherical (but non-expanding) waves generated by pairs of particles with arbitrary multipole structure propagating in opposite directions. When the cosmological constant is negative, they are hyperboloidal waves generated by a null particle of the same type. In this case, they are included in the impulsive limit of a class of solutions described by Siklos t…
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Instituto de Ciencias Exactas y Naturales, Universidad Arturo Prat（阿图罗·普拉特大学精确科学与自然学院）；Facultad de Ciencias, Universidad Arturo Prat（阿图罗·普拉特大学理学院）；Departamento de Física, Cinvestav（墨西哥国立理工学院先进研究中心物理系）
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