Abstract
Abstract
We prove that any real, vacuum gravitational perturbation of a four-dimensional vacuum pp-wave space-time can be locally expressed, modulo gauge transformations, as the real part of a Hertz/Debye potential, where the scalar potential satisfies the wave equation. We discuss relations with complex perturbations, complex space-times, non-linear structures, and real spaces with split (ultra-hyperbolic/Kleinian) signature. Motivated by generalized notions of parallel spinors, we also discuss generalizations of the result to other space-times.
Subject
Physics and Astronomy (miscellaneous)
Reference25 articles.
1. Differential geometry and relativity;Penrose,1976
2. Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor;Bryant,2000
3. On the geometry of Petrov type II spacetimes;Aksteiner;Class. Quant. Grav.,2021
4. Self-duality and gravitational perturbations;Castillo;J. Math. Phys.,1999
5. Zero rest mass fields including gravitation: asymptotic behavior;Penrose;Proc. Roy. Soc. Lond. A,1965