= Euclidean horizon period under a regular radial conformal factor
{c}
{title2=$\beta=4\pi/|f'(r_H)|$}
For a Euclidean radial-time metric $C(r)(f(r)dt_E^2+dr^2/f(r))$, assume $f$ has a simple horizon zero and $C$ is smooth, finite and positive there. A proper radial coordinate $\rho=2\sqrt{C(r_H)(r-r_H)/f'(r_H)}$ puts the leading metric in the form $d\rho^2+f'(r_H)^2\rho^2dt_E^2/4$. Smoothness fixes the displayed period independently of $C(r_H)$. When the Lorentzian time is normalized at infinity, the period is the inverse <Hawking temperature> in natural units. A conformal factor singular at the horizon need not preserve this argument.
// Target: general-relativity.bigb
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