On Sat, Jan 25, 2014 at 1:25 PM, Richard Ruquist <[email protected]> wrote:
> > > > On Sat, Jan 25, 2014 at 12:02 PM, meekerdb <[email protected]> wrote: > >> On 1/25/2014 5:29 AM, Edgar L. Owen wrote: >> >>> Brent, >>> >>> We have to be careful to be precisely accurate here. >>> >>> 1. The structure of a black hole is not just a singularity inside an >>> event horizon. The entire interior of a black hole is not a singularity. >>> The singularity exists only at the very center of a black hole, there is >>> plenty of volume between the event horizon and the singularity. >>> >> >> Actually there is plenty of *time* between the horizon and the >> singularity - if the black hole is large enough. The singularity isn't at >> a different place, it's in the future, once you're inside the event horizon. >> > > At least for a spherically symmetric black hole, the GR solution indicates > that the time dimension becomes the radial dimension of the black hole. > Thus time vanishes inside the event horizon of a spherical black hole. > It would be more correct to say that the "time" dimension of the Schwarzschild coordinate system becomes spacelike, so inside the horizon, a path through spacetime that has a constant "position" coordinate but a varying "time" coordinate would actually be a spacelike path (the question of whether a path through spacetime is timelike, spacelike, or lightlike is one that has an objective answer that doesn't depend on the choice of coordinate system, see https://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals and https://en.wikipedia.org/wiki/Spacetime#Spacetime_in_general_relativity ). However, it is likewise true in Schwarzschild coordinates that the "radial" dimension becomes timelike, so inside the horizon a path with a constant "time" coordinate but varying "radial" coordinate would be a timelike path. So, time in a physical sense doesn't actually vanish inside the horizon, it's just that the coordinate separation between ticks of your clock would be best measured using the "radial" coordinate of Schwarzschild coordinates, not the "time" coordinate. Also note that this is just a quirk of how Schwarzchild coordinates are defined, you can define other coordinate systems on the same curved spacetime that don't have this issue, like Kruskal-Szekeres coordinate: https://en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates#Qualitative_features_of_the_Kruskal-Szekeres_diagram In KS coordinates the "time" coordinate remains timelike inside the horizon, and the "radial" coordinate remains spacelike (these coordinates also have the nice feature that worldlines of light rays always have a 45 degree angle on the coordinate diagrams, just like in diagrams of inertial coordinate systems in special relativity). And in principle, even in the ordinary flat spacetime of special relativity you can define some kind of non-inertial coordinate system where a coordinate that is timelike in one region switches to becoming spacelike in another, and vice versa--this sort of thing isn't any type of physical effect, it's just due to the way you define your coordinate system. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
