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The line element of a black hole is given by: [tex]ds^2=\Bigg(1-\frac{2m}{r}\Bigg)d\tau ^2+\Bigg(1-\frac{2m}{r}\Bigg)^{-1} dr^2+r^2\Big(d\theta ^2+\sin^2(\theta)d\phi ^2\Big)[/tex]

It has an apparent singularity at ##r=0##. By making ##\tau## an angular coordinate, show that this singularity is a coordinate singularity (not physical) and find the period of ##\tau## that makes it possible. (consider expanding the metric functions about ##r=2m##).

Thanks for the help!!!