Hello everyone, I have a question regarding the possible periodicity of time in a generic metric.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that for some reason I have a solution to Einstein's equations of the kind (in Euclidean time):

$$

ds^2_E=+f(r)dt_E^2+\frac{dr^2}{g(r)}+r^2(dx^2+dy^2).

$$

Am I always allowed to assign some periodicity to the Eucledean time ##t_E## or is there any restriction?

For example, I know that there is a particular solution called "thermal AdS" which is nothing but the usual AdS metric (i.e. not a black hole with an horizon) to which a periodic time has been assigned.

When can I do that?

Thanks!

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# Periodic time for a generic soliton solution

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