- Summary
- Rindler coordinates result in T=0/0 when a=0. Is there a clean way to fix that?

Rindler coordinates are nice, but they fall apart when a=0, where ##T=\frac{sinh(at)}{a}=\frac{0}{0}##. Is there a good way to fix that?

Intuitively I'd want to do out the taylor expansion, divide by a, then collapse it back to... something...

$$T=\frac {\sinh(at)} {a}=\frac{ \sum_{n=0}^\infty {\frac {(at)^{2n+1}}{ (2n+1)!}}} {a} = \sum_{n=0}^\infty {\frac {a^{2n}t^{2n+1}} {(2n+1)!}} = ???$$

Is there any simplification of that taylor expansion to something sane that doesn't result in 0/0?

Is there another approach which might work better?

Intuitively I'd want to do out the taylor expansion, divide by a, then collapse it back to... something...

$$T=\frac {\sinh(at)} {a}=\frac{ \sum_{n=0}^\infty {\frac {(at)^{2n+1}}{ (2n+1)!}}} {a} = \sum_{n=0}^\infty {\frac {a^{2n}t^{2n+1}} {(2n+1)!}} = ???$$

Is there any simplification of that taylor expansion to something sane that doesn't result in 0/0?

Is there another approach which might work better?