On the distinction between coordinate and physical speed of light in General Relativity

The present paper has a pedagogical aim. On this basis, we will discuss the concept of velocity in General Relativity and try to explain it using some well-known metrics in the scientific literature. While none of the examples in this work is new except for the last one, such a systematic treatment could be a useful contribution to the teaching of General Relativity at an introductory level. In particular, in the last section, we will focus on rotating coordinates and give our interpretation within this framework