Parallel spinors, pp-waves, and gravitational perturbations
arXiv:2204.13673 · doi:10.1088/1361-6382/acaa83
Abstract
We prove that any real, vacuum gravitational perturbation of a 4-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.
arXiv comment15+5 pages, 1 figure
References in corpus (11)
- Anti-self-dual four-manifolds with a parallel real spinor
- Hyper-K{ä}hler Hierarchies and their twistor theory
- Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor
- The mass and angular momentum of reconstructed metric perturbations
- On the Existence of Radiation Gauges in Petrov type II spacetimes
- Linear perturbations of Hyperkahler metrics
- Tails of plane wave spacetimes: Wave-wave scattering in general relativity
- Conformal invariance, complex structures, and the Teukolsky connection
- On the geometry of Petrov type II spacetimes
- Conformal geometry and half-integrable spacetimes
- Curvature without metric: the Penrose construction for half-flat pp-waves