A note on the index notation used in posts on relativity. In many of my posts, I was lazy and used Roman rather than Greek letters for tensor indices, as they are easier to type in Latex. The convention in most textbooks on relativity is to use Greek indices for the four components of spacetime, and Roman indices when referring only to spatial coordinates. Apologies for this, but it would be far too much work to go through all the posts and convert everything to Greek letters. In most cases, there shouldn't be any confusion, as in almost all posts, we're talking about the four dimensions of spacetime.
The conventions for distinguishing between 4-vectors (with four spacetime components) and 3-vectors (in regular 3-d space) vary from one book to another, and I usually use the convention that was used in the book that was my primary source for a post. Moore represents 4-vectors by boldface font, which is usually reserved for 3-vectors in other texts. Schutz uses ordinary font for 4-vectors and a little arrow over the letter for 3-vectors. Always check the conventions for whatever book you're using.