Timeline for A question about black hole interior
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 5, 2019 at 8:02 | vote | accept | Wein Eld | ||
| Aug 5, 2019 at 6:49 | comment | added | A.V.S. | … these coordinates are angular coordinates … like I said, these are not angles. You could interpret $\theta$ and $\phi$ as angles only if there is a point near which the spatial metric behaves like $dr^2+r^2(d\theta^2+\sin^2\theta d\phi^2)+\text{h.o.t.}$ (h.o.t. -higher order terms). There is no such point on the slice $\tau=\text{const}$, $a(t)$ is constant on this slice. | |
| Aug 5, 2019 at 6:28 | comment | added | Wein Eld | But these coordinates are angular coordinates, shouldn't it be natural that along with them the space is compact? If this logic validates, then the spatial hyperbolic slice in flat spacetime is also not isotropic. Is that true? | |
| Aug 5, 2019 at 6:24 | comment | added | Wein Eld | At the slice $\tau$=const, we have three spatial coordinates $\xi$,$\theta$ and $\phi$. Certainly $\xi$ is special compared with the other two because it is the radial coordinate while $\theta$ and $\phi$ are the angular coordinates. And I do not understand what do you mean by "the space is infinite along the $\xi$ coordinate and it is clearly finite in any direction orthogonal to it". I assume the directions orthogonal to $\partial_\xi$ are $\partial_\theta$ and $\partial_\phi$ (because there are no terms like $d\xi d\theta$ in the metric). | |
| Aug 5, 2019 at 6:09 | comment | added | Wein Eld | Thanks for your answer but I am not sure I fully agree with it. I now understand the difference between “there are no θ- and ϕ-dependencies” and isotropy. But I still cannot see why the spacetime you wrote down is not isotropic. You argue that within the slice $\tau=const$, directions are not equivalent by taking the example on $\partial_\xi$. | |
| Aug 4, 2019 at 18:56 | history | answered | A.V.S. | CC BY-SA 4.0 |