Optics in a nonlinear gravitational plane wave

Abstract

Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.

32 pages, minor additional explanations

References in corpus (7)

• The Confrontation between General Relativity and Experiment
• An electromagnetic analog of gravitational wave memory
• Fermi Coordinates and Penrose Limits
• Optical frequency standards for gravitational wave detection using satellite Doppler velocimetry
• The rotation of polarization by gravitational waves
• Gravitational wave detector response in terms of spacetime Riemann curvature
• Effects of rotating gravitational waves

Cited by in corpus (20)

• Soft Gravitons & the Memory Effect for Plane Gravitational Waves
• Persistent gravitational wave observables: general framework
• Memory, Penrose Limits and the Geometry of Gravitational Shockwaves and Gyratons
• Persistent gravitational wave observables: Nonlinear plane wave spacetimes
• Scaling and conformal symmetries for plane gravitational waves
• Generating exact solutions to Einstein's equation using linearized approximations
• Memory effect, conformal symmetry and gravitational plane waves
• The First-Order Velocity Memory Effect from Compact Binary Coalescing Sources
• Large Gauge Effects and the Structure of Amplitudes
• Ion Traps and the Memory Effect for Periodic Gravitational Waves
• Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields
• Persistent gravitational wave observables: Nonlinearities in (non-)geodesic deviation
• Average nonlinear dynamics of particles in gravitational pulses: effective Hamiltonian, secular acceleration, and gravitational susceptibility
• Gravitational wave memory and its effects on particles and fields
• A New Twist on the Geometry of Gravitational Plane Waves
• Testing the Wave-Particle Duality of Gravitational Wave Using the Spin-Orbital-Hall Effect of Structured Light
• Dynamics, quantum states and Compton scattering in nonlinear gravitational waves
• Elliptically Polarized Plane Gravitational Waves
• Spin vector deviation and the gravitational wave memory effect between two free-falling gyroscopes in the plane wave spacetime
• Blueshift of light rays induced by gravitational wave memory effect