The main problem with papers like this, and they are very typical, is that they assume a vast background of esoteric knowledge of the subject and quote equations from previous work which most people would not be familiar with unless a specialist in the field. What the author is claiming (I think) is that by using metamaterials whose refractive indices are not a simple number but depend on the orientation and defined as a tensor, the behavior can be analogous to curved space defined by a mathematically similar tensor. Light passing through such a region can behave similarly to a mass in an mathematically analogous metric.