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Another book by Greg Egan exploring different metrics of spacetime is Dichronauts.

In Orthogonal the metric signature explored is (+,+,+,+).

In Dicronauts the metric signature explored is (-,-,+,+).

(We live in a universe with metric signature (-,+,+,+).)

http://gregegan.net/DICHRONAUTS/DICHRONAUTS.html

What would the difference between (-,+,+,+) and (+,-,-,-) be? It seems like they are the same except for choice of labels. I guess the main difference is where speed of light fits in. In (-,+,+,+) the - is multiplied by c.

You are right, there is no difference.

As a matter of fact, many physicists work with a signature of (+,-,-,-) to describe the spacetime of our universe.

https://en.wikipedia.org/wiki/Sign_convention#Relativity

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