pp-waves in modified gravity

Abstract

The family of metrics corresponding to the plane-fronted gravitational waves with parallel propagation, commonly referred to as the family of pp-wave metrics, is studied in the context of various modified gravitational models in a self-contained and coherent manner by using a variant of the null coframe formulation of Newman and Penrose and the exterior algebra of differential forms on pseudoRiemannian manifolds.

Dynamics of a fermion with dipole moments in external wave fields

“…Similarly, the plane gravitational wave [30,31] is described by the corresponding gravitational field strengths, the torsion T ij α and the curvature R ij αβ , that satisfy…”

A derivation of Weyl-Lanczos equations

“…where the numerical indexes refer to the null coframe. The self-dual part of the curvature corresponding to the k ∧ m component corresponds to the only nonvanishing Weyl tensor component [27][28][29]. For vacuum, the Einstein field equations are satisfied if H ζζ = 0, so that Ω 1 2 = C 1 2 = H ,ζζ k ∧ m (82) in this case.…”

Congruence Convergence in Pp-Wave Space–Time

“…Now for affinely parameterized geodesic congruences, the Raychaudhuri equation in Eq. (14) can be recast by calculatingΘ = D dτ ( µ ;µ ) as below:…”