Whack-a-Mole
For an infinite universe, expanding does not mean getting bigger. Things are just spreading out.
I can’t answer your first point, but to the second, light standing still does not imply no future. If you emit a pulse of light, the path it takes is your future light cone. Your future lies inside the future light cone. If you are at or inside the event horizon and emit a pulse of light, it stays inside the horizon and eventually hits the singularity. Your future would remain inside the horizon and you would end up at the singularity. Time would not stand still for you. It would end when you hit the singularity.
Bingo! The “arbitrary vantage point” is a general reference frame where light (in a vacuum) can stand still. In an inertial reference frame falling into the hole, the light would be traveling at c.
barbitu8,
Don’t be tachy. Yes, you can take the equations of GR and SR and let velocity be greater than c, but you invoke causality violations and you get all sorts of strange results like imaginary lengths and times. It is usually assumed that nothing travels faster than light.
Is that a pun on tachyons, which I think is the name given to hypothetical objects that do go faster than light. So I don’t think the “usually assumed” is correct. It would take infinite energy to accelerate an object to go faster than light, and it would take infinite energy to decelerate an object to go slower if it were going faster. Since, that is impossible, it is impossible to do so. So there is no invocation of causality violations. In fact, I believe that astrophysicists believe that tachyons do, in fact, exist.
If information can be transferred between objects traveling slower than light and objects traveling faster than light, you will have causality violations. If information cannot be transferred, then in what sense do they exist?
Does the physics of black holes have anything to say about a black hole getting too big? Big enough, that is, to change the very nature of space? (Or the very nature of what we call time?)
A black hole of any size changes the very nature of space and time. Space and time are profoundly different inside the black hole. An object inside the event horizon must get closer to the singularity. The distance to the singularity behaves like a time coordinate in that you can only travel that dimension in one direction (towards the singularity). Also, anything inside the event horizon has a finite future. Outside the horizon, space and time behave just like they do around any gravitational field.
Is the word singularity the same “singularity” as in found in Complex Analysis? (IIRC, an infinity in an integration?)
Is there any mathematics which deals with what happens “at” the singularity? Is what someone speculated earlier, (that a particle/photon will suffer a “time dilation”–by which I understand “will never reach the singularity”), correct? If not, does everything (theoretically) “pile up” at the singularity like some gigantic B-E blob? (Sorry, don’t mean to ask too many questions.)
As I understand it all known laws of physics fall apart at those scales. I’m not positive but I think the Planck Limit defines (roughly) the point at which us mere humans can no longer describe or predict via math or anything else what is happening.
I think a quantum theory of gravity is what is needed to delve deeper into these mysteries but so far we don’t have one yet.
The problem is that time stops at the singularity. Inside the horizon, the time axis points toward the singularity. At the singularity time does not exist; there is no way to measure time. This is quite different from time dialation where time slows down. When you experience time dialiation, you don’t notice it. Time dialation only exists relative to some other observer. You cannot place an observer at the singularity. Any clock would be crushed out of existance when it reaches the singularity.
At the singularity, time ends.
I can’t seem to find a definition of singularity, but I’m pretty sure that it is the same thing as in complex analysis: where some of your coordinates do not have valid values.
In B-E condensation the individual particles all assume the same quantum values, but they are still the same particle. At the singularity, everything loses its identity.
The singularity is just due to the fact that as r becomes small, 1/r is large, and 1/r shows up in the description of a black hole. In complex analysis, you’d say that there’s a simple pole at r=0. Classically, you’d be at a region where the strength of gravity would be infinite, and everything’d be crushed into one tiny but very massive thing. Naturally, however, before you get there, you run into the problems with needing quantum mechanics to which Whack-a-Mole alluded.
There are two different types of “singularity” in general relativity, with different interpretations. A physical singularity is one in which some locally-measurable physical parameter (spacetime curvature, for the singularity at the center of a black hole) becomes infinite, probably indicating that classical GR is inadequate to explain the physics here. A coordinate singularity is more like what you describe, where the local system of coordinates you chose no longer accurately represents spacetime. This can happen where some of the coordinates blow up (such as at the event horizon, for an observer at rest relative to the BH) or are undefined (such as at the poles in spherical coordinates). Coordinate singularities aren’t always meaningless–the event horizon is a good example–but they are not locally detectable (unlike physical singularities, which can be detected by local measurements).
Nitpick: Any orbit that doesn’t intersect the bowling ball on the first orbit will be an elliptical orbit that lasts ‘forever’, at least in Newtonian mechanics. As you mention, in general relativity all closed orbits decay, so any orbit that doesn’t immediately hit the bowling ball will either last forever (Newton), or will eventually spiral into the bowling ball (Einstein).