Stand up in a clear space and spin round. It is not too difficult to turn at one revolution each two seconds. Suppose the moon is on the horizon. How fast is it spinning round your head? It is about 385,000
km away so the answer is 1.21 million km/s, which is more than four times the speed of light! It sounds ridiculous to say that the moon is going round your head when really it is you who is turning, but
according to general relativity all co-ordinate systems are equally valid including revolving ones. So isn't the moon going faster than the speed of light? This is quite difficult to account for.
What it comes down to, is the fact that velocities in different places cannot be directly compared in general relativity. Notice that the moon is not overtaking the light in its own locality. The velocity of the
moon can only be compared to the velocity relative to other objects in its own local inertial frame. Indeed, the concept of velocity is not a very useful one in general relativity and this makes it difficult to
define what "faster than light" means. Even the statement that "the speed of light is constant" is open to interpretation in general relativity. Einstein himself in his book "Relativity: the special and the
general theory" said that the statement cannot claim unlimited validity (pg 76). When there is no absolute definition of time and distance it is not so clear how speeds should be determined.
Nevertheless, the modern interpretation is that the speed of light is constant in general relativity and this statement is a tautology given that standard units of distance and time are related by the speed of
light. The moon is given to be moving slower than light because it remains within the future light cone propagating from its position at any instant.