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I'm reading these notes:

http://arxiv.org/PS_cache/gr-qc/pdf/9707/9707012v1.pdf

and have a few questions.

(i) On page 11, why is equation (2.1) true? Where does this come from? I guess the timelike feature manifests itself as the minus sign at the front but I could really just use some help on understanding this equation.

(ii) Why does [itex]d \tau = \sqrt{ - ds^2}[/itex] as is written in (2.2)?

(iii) Where does (2.6) come from? What does he mean by [itex]D_{(\lambda)}[/itex]?

I can see he's tried to define it in (2.7) but that's not really helping much!

Thanks.