sbaker8688 said:
On a penrose diagram, we are representing 1D space (x-axis) across time (y-axis) (I get that there is 'warpage' or 'compactification' going on - forget that for the moment). True, or False?
Mu. "1D space" and "time" do not have invariant meanings. A Penrose diagram is drawn in a particular set of coordinates; and you are correct that to the extent that the diagram does represent "1D space (x-axis) across time (y-axis)"
in those coordinates. But those coordinates do not have any straightforward physical meaning. The only straightforward physical meaning that can be read off a Penrose diagram is, as I said in post #2, that lightlike curves are always 45 degree curves, so causal boundaries--boundaries of what regions of spacetime can or cannot send or receive light signals to or from what other regions of spacetime--are easily seen. But nothing else about the "space" or "time" of the diagram corresponds to anything you are used to.
sbaker8688 said:
if I'm understanding the diagram above correctly, the black hole is growing.
You're not understanding the diagram correctly. I already explained why in post #2. The "event horizon" line marks a line at which
every point represents a 2-sphere with the
same surface area (##4 \pi r_s^2##, where ##r_s## is the Schwarzschild radius of the black hole). So every point on that line represents a 2-sphere of the same "size". (Actually, that's only true for the portion of the horizon outside the collapsing matter that formed the hole. More on that below.)
sbaker8688 said:
You can't just drop a black hole in the middle of a penrose diagram
Yes, you can. Your proposed "solution" is not correct. The diagrams you showed in post #6 are
correct Penrose diagrams of a black hole, as far as they go. One thing they do leave out is the collapsing matter that formed the hole in the first place. For a diagram that shows that, see the OP of this thread:
https://www.physicsforums.com/threa...ck-hole-with-a-changing-event-horizon.968233/
The area shaded in blue represents the region of spacetime occupied by the collapsing matter. Note that the diagram is not strictly correct: the blue shaded area should narrow down to the top left corner, right where the vertical r = 0 line at the left edge meets the wiggly r = 0 singularity line at the top. That top left corner point represents the event at which the collapsing matter reaches zero size and vanishes, forming the singularity.
Note also that the event horizon line is still a 45 degree line going up and to the right; but it starts at the r = 0 line on the left
inside the collapsing matter. In fact, that event, where the event horizon starts at the r = 0 line, is the specific event where the event horizon forms, at the center of the collapsing matter; the horizon then expands outward until it reaches the surface of the collapsing matter (the point where it crosses the outer right edge of the blue shaded area). Once the horizon exits the surface of the collapsing matter, it remains the same size afterwards (the size--surface area--that I gave above). At least, it does provided no other matter falls in; the thread linked to above discusses what happens in the case that more matter does fall in.
Another prior thread on Penrose diagrams is here:
https://www.physicsforums.com/threads/penrose-diagrams-introduction.699126/
sbaker8688 said:
these drawings often depict black holes way out at infinity, on the edge of the diagram.
No, they don't, although Penrose diagrams can be confusing in this respect. The point marked ##i^+## on the diagram, which is future timelike infinity, does
not connect with either the event horizon or the singularity. If you zeroed in on that area of the diagram, you would see the singularity ending in a point, the event horizon ending in a separate, disconnected point just to the right of it, and the ##i^+## point as another separate, disconnected point to the right of that.
sbaker8688 said:
the event horizon is expanding at the speed of light in these drawings
No, it's not. The event horizon is an outgoing null surface, i.e., it is made of radially outgoing light rays, but it is
not expanding; its surface area stays constant (once it is outside the collapsing matter that formed the hole). The reason a surface made of radially outgoing light rays can be not expanding and maintain a constant surface area is the spacetime curvature of the hole.