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BTZ black hole

{c}

For
$$
ds^2=-fdt^2+\frac{dr^2}{f}+r^2(d\phi-\Omega dt)^2,
$$
the transformations $dv=dt+dr/f$ and $d\chi=d\phi+\Omega\,dr/f$ give
$$
ds^2=-f\,dv^2+2\,dv\,dr+r^2(d\chi-\Omega\,dv)^2,
$$
which is regular at every horizon where $f$ vanishes while $\Omega$ remains finite.


Ingoing BTZ coordinates

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 311 / 1 / b / Solution

Ingoing BTZ coordinates

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Ingoing BTZ coordinates

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