Gravitational lensing beyond geometric optics: II. Metric independence

Understand

Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate.

• Nevertheless, the optical fields themselves - as opposed to their interactions with material bodies - encode very little of that geometry: It is shown here that any given configuration is compatible with a very large variety of spacetime metrics.
• For scalar fields in geometric optics, or observables which are not sensitive to the detailed polarization content of electromagnetic or gravitational waves, seven of the ten metric components are essentially irrelevant.
• With polarization, five components are irrelevant.