Including Absorption in Gordon's Optical Metric

TL;DR

This paper extends Gordon's optical metric to include absorption by making it complex, enabling better modeling of light propagation in absorbing media and offering alternative explanations for supernova observations.

Contribution

It introduces a complex generalization of Gordon's optical metric to incorporate absorption effects in curved spacetime.

Findings

Derived corrected distance-redshift relations for cosmological models.

Fitted supernova data with absorption effects, suggesting alternatives to dark energy.

Demonstrated the applicability of complex optical metrics in geometrical optics.

Abstract

We show that Gordon's optical metric on a curved spacetime can be generalized to include absorption by allowing the metric to become complex. We demonstrate its use in the realm of geometrical optics by giving three simple examples. We use one of these examples to compute corrected distance-redshift relations for Friedman-Lema\^itre-Robertson-Walker models in which the cosmic fluid has an associated complex index of refraction that represents grey extinction. We then fit this corrected Hubble curve to the type Ia supernovae data and provide a possible explanation (other than dark energy) of the deviation of these observations from dark matter predictions.