Spatial dimensions inside a black hole

[atrchi]

hello all

I am so glad to have found this forum. I've always had an interest in astrophysics, cosmology, SR/GR, etc, and no place to ask questions. I'm an engineer and was once a member of Mensa (I only left the organization because I thought other members were crazy. Sorry). So although I'm an amateur at this stuff, I hope my questions are worthy of your consideration.

I've been reading lately a lot about black holes, and something that caught my interest, is the interpretation of the Schwarzschild metric which says r becomes a time-like dimension for an infalling observer past the event horizon. I read somewhere else that the Schwarzschild metric was originally only thought to be valid outside the event horizon, but later work using different coordinates was able to connect the outside to the inside, so I assume the time-like characteristics of r inside the radius are still a worthwhile area of scientific investigation (note, to those who believe that science has no business investigating things that are outside the observable universe, as the inside of black holes is to our frame of reference, I retort: if we don't try to understand what the inside of a black hole looks like, we'll never be able to assert that we are not inside one).

So, that leads me to a few questions...

What happens to the other time dimension when r becomes time-like? Does space still have 3 dimensions? (assume the frame of reference is either an invincible infalling observer, or, intelligent life that might evolve locally after the crossing of the event horizon)

If so: Does that mean one of the finite space dimensions suddenly become infinite by taking over the old time dimension? For an infalling observer (invincible, or intelligent life evolved after crossing of the horizon), would this expansion of finite space to infinite space be mathematically distinguishable from the big bang as experienced in our current universe?

Does spaghettification in the spatial dimensions stop at some radius when the bulk of the gravitational pull is in the time-like direction? Mathematically speaking is this any different from our current universe, where we're all spaghettified in the time dimension?

Again, assuming a time-like r... when more matter arrives in a black hole, does it arrive in the past relative to observers that are already inside? If a constantly changing past affects the future inside the black-hole, that would have interesting anthropic implications, no?

Thank you for your patience. I've been looking for this forum all my life :-)

 

[ImaLooser]

hello all

I am so glad to have found this forum. I've always had an interest in astrophysics, cosmology, SR/GR, etc, and no place to ask questions. I'm an engineer and was once a member of Mensa (I only left the organization because I thought other members were crazy. Sorry). So although I'm an amateur at this stuff, I hope my questions are worthy of your consideration.

I've been reading lately a lot about black holes, and something that caught my interest, is the interpretation of the Schwarzschild metric which says r becomes a time-like dimension for an infalling observer past the event horizon. I read somewhere else that the Schwarzschild metric was originally only thought to be valid outside the event horizon, but later work using different coordinates was able to connect the outside to the inside, so I assume the time-like characteristics of r inside the radius are still a worthwhile area of scientific investigation (note, to those who believe that science has no business investigating things that are outside the observable universe, as the inside of black holes is to our frame of reference, I retort: if we don't try to understand what the inside of a black hole looks like, we'll never be able to assert that we are not inside one).

So, that leads me to a few questions...

What happens to the other time dimension when r becomes time-like? Does space still have 3 dimensions? (assume the frame of reference is either an invincible infalling observer, or, intelligent life that might evolve locally after the crossing of the event horizon)

If so: Does that mean one of the finite space dimensions suddenly become infinite by taking over the old time dimension? For an infalling observer (invincible, or intelligent life evolved after crossing of the horizon), would this expansion of finite space to infinite space be mathematically distinguishable from the big bang as experienced in our current universe?

Does spaghettification in the spatial dimensions stop at some radius when the bulk of the gravitational pull is in the time-like direction? Mathematically speaking is this any different from our current universe, where we're all spaghettified in the time dimension?

Again, assuming a time-like r... when more matter arrives in a black hole, does it arrive in the past relative to observers that are already inside? If a constantly changing past affects the future inside the black-hole, that would have interesting anthropic implications, no?

Thank you for your patience. I've been looking for this forum all my life :-)

There is a professor at UC Boulder who studies these things. The concept of time is very strange inside the event horizon of a black hole. He says that matter goes both backward and forward in time. He has done a good deal of work on all this, and you might like that. He has some videos on Youtube as well.

 

[atrchi]

Do you have a name I can Google? Thanks!

 

[ImaLooser]

Do you have a name I can Google? Thanks!

No, but "UC Boulder" and "black hole" ought to do it.

 

[atrchi]

OK must be this guy... Andrew Hamilton http://casa.colorado.edu/~ajsh/
Interesting links.

 

[George Jones]

Welcome to Physics Forums!

I've been reading lately a lot about black holes, and something that caught my interest, is the interpretation of the Schwarzschild metric which says r becomes a time-like dimension for an infalling observer past the event horizon.

Are you familiar with Johnny Cash's song "A Boy named Sue"?

There is nothing strange going here except the names chosen by humans (not by nature!) for particular coordinates. The metric tells all! The metric tells us that:

1) inside the event horizon, [itex]r[/itex] is a timelike coordinate;

2) inside the event horizon, [itex]t[/itex] is a spacelike coordinate;

3) humans made a dog's breakfast of things when they chose labels for particular coordinates inside the event horizon.

 

[Kraflyn]

Hi.

You should realize Schwarzshild metric is singular at horizon. One cannot extend it beyond singularity, just like one cannot use complex function's representation outside its disk of convergence. One transforms coordinates into more suitable ones to examine what happens beyond "horizon". Horizon exists for outside observer, but not for ingoing observer. What about inside observer? Metric valid for outside observer is invalid for an inside observer and vice versa. The situation is similar to complex analysis. If You try to use series defining some complex function outside it's region of convergence, You will get funny results.

Cheers.