- #1
Einj
- 470
- 59
Hello everyone, I have a question regarding the possible periodicity of time in a generic metric.
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!
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!