Starship Asterisk*

I guess the best way I "might" describe it as analogous to hyperspace being the next dimension up from our three sensory perceptions except in reverse – a negative "hypo space". The only way I've been able to mentally imagine hyper space is the hyper cube.
Hence a black hole's gravity "might" be better represented by a negative hypo-sphere if that' possible to think of. Sorry this is off the cuff - I'm not trying to invent a concept. And don't ask me to draw one. That would actually be worse than me trying to describe it but not nearly as hard to believe.

Thinking of it terms of potential energy is actually much easier than my way. Thanks!!

Ron-Astro Pharmacist wrote:I was asking wouldn't the "falling in" really be occurring in all directions; not just down as in the picture? I know the above is just an attempt to visualise the concept but when used over and over I wonder if we, perhaps, misrepresent the spacetime distortion in our minds to be uni-directional.

This image is treating space as two-dimensional with a fictitious gravity-like force acting "downwards". In reality, the distortion of spacetime that is responsible for gravity operates in four dimensions (three spatial dimensions). There is no obvious "down" in that situation.

The point is, the intent is to introduce the concept of warped space. That is useful for understanding certain things about the nature of gravity, but not particularly for understanding it from a behavior standpoint. In that sense, it's nothing more than an attractive force that operates on mass and follows an inverse square law for magnitude.

If a picture is worth a thousand words in literature then an equation is probably worth a thousand pictures in astrophysics. Thanks Chris!!

Good luck with your hyper sphere – I'm looking forward to the answer to "It's a Bird, It's a Plane" in the Open Space forum. It'll probably be U = FO but we can always hope.

I'll take a stab at this, in hopes that I understand Ron's question. Imagine a compact, spherical, massive body in space and that nothing much else is there to confuse the simple situation. Draw the plane that passes through its center and the observer's eyes. The diagrams in your post graph the potential energy level at the points in that plane. If you arbitrarily give a zero value to the potential at some given distance from the body, then the diagrams plot a graph of points above or below zero at that point. The "up" direction in the diagram is simply the direction used to plot increasing potential, which is being graphed. The curvy sheets are the surface of the potential function.

So, a tiny traveller moving in the plane I described, would undergo the changing levels of potential energy with respect to the gravity well as depicted in the warped sheets of those diagrams. Of course the diagram just depicts life in one plane. If you draw any other plane through the massive object, the potential diagram needs to be re-oriented for it. So, you're right, of course, it is the same from any direction. But I have no idea how someone could make a diagram that depicted that, but was still a useful, legible graph depicting much of anything clearly.

ta152h0 wrote:re black holes still considered a singularity ?

At the "center" of a black hole the theory that describes them, general relativity, breaks down because of a singularity. Everywhere else is fine, in particular at the event horizon, which marks the "point of no return". This is also what allows one to simulate today's APOD.

ta152h0 wrote:And has the star movement been deciphered at the center of our own galaxy ?

Yes. From the orbit of stars close to the galactic center (see, for example, Fig 13 in the reference) one can deduce that there is a black hole at the center with a mass of about 4 million solar masses.

Markus, is the singularity simply the spot where the math breaks down? Another way of asking the same question: is there a mass at the center of the black hole which has a diameter > 0, however small it might be?

Rob

rstevenson wrote:Markus, is the singularity simply the spot where the math breaks down? Another way of asking the same question: is there a mass at the center of the black hole which has a diameter > 0, however small it might be?

The math says all the mass is at a dimensionless point at the center. That's what defines a singularity, and that's where the theory breaks down.

Of course, we have no idea if there is a physical singularity in the center of a black hole, or some sort of exotic particle, or mass in some exotic state, or what.

rstevenson wrote:Markus, is the singularity simply the spot where the math breaks down? Another way of asking the same question: is there a mass at the center of the black hole which has a diameter > 0, however small it might be?

Rob

The concept of a singularity of a space-time is mathematically well defined. But the definition is rather abstract and not immediately intuitive. Yes, it's the spot where the math/physics goes boink. Roughly, once a particle passes the event horizon, it will continue to travel to the "center" of the black hole. It cannot reverse its course for the same reason we can't go back in time. As a consequence, everything that falls into a black hole will end up at the "center". We then have a finite amount of mass (like 4 million solar masses) at a single point. This creates an infinite energy density (finite mass/0 volume), which in turn, due to general relativity, means also an infinite space-time curvature. But an infinite curvature contradicts the assumption of a smooth space-time, hence general relativity is no longer valid. Another way to view this is to say that there is no center (because it as unphysical properties), but then you can show rigorously that you can fall over the edge of space-time in a finite amount of proper time

As is often the case when infinities arise in physics, it is reasonable to expect that general relativity is just not valid at the "center". Once matter is compressed to such small dimensions, you can't ignore quantum theory. A quantum theory of gravity could then solve all the problems with infinities and have physically reasonable properties. Alas, all attempts to properly combine general relativity and quantum physics have lead to even more infinities...

Markus Schwarz wrote:Roughly, once a particle passes the event horizon, it will continue to travel to the "center" of the black hole.

This has always seemed off to me. In reality, I'd expect that a good deal of mass inside the event horizon (maybe all of it) must actually be in relativistic orbits around the center. As it sheds energy to collisions and gravitational waves, it will get closer and closer to the center. But how long does it take a subatomic particle to actually intersect a dimensionless point, and what happens when it does? It's not clear to me how anything ends up in the center.

Chris Peterson wrote:

Markus Schwarz wrote:Roughly, once a particle passes the event horizon, it will continue to travel to the "center" of the black hole.

This has always seemed off to me. In reality, I'd expect that a good deal of mass inside the event horizon (maybe all of it) must actually be in relativistic orbits around the center. As it sheds energy to collisions and gravitational waves, it will get closer and closer to the center. But how long does it take a subatomic particle to actually intersect a dimensionless point, and what happens when it does? It's not clear to me how anything ends up in the center.

This is best discussed mathematically in Kruskal-Szekeres coordinates. The wikipedia article does a good job at discussing the physics, IMHO. Notice that in these coordinates the singularity does not appear as a point but as a hyperbola. In these coordinates, showing that any particle inside the black hole reaches the singularity is transformed into showing that a line intersects a hyperbola.

Of course, this applies only to the Schwarzschild black hole. Once you start to consider a rotating black hole (and this if also the more realistic scenario) things get more involved. I don't know if stable trajectories inside it are possible or not.

Lightcone variant (per Wiki link)
In the literature the Kruskal–Szekeres coordinates sometimes also appear in their lightcone variant:

So if UV =O and V = constant = Future (F) then UF = O at some time in the future. (I thought so)

I was close.

Sorry - forgive me my attempt at humor(and don't believe a word I type) except that I really do say thanks for all your comments as I try to digest them. Ron

This picture shows how nothing happens or exists inside a black hole. Space-time bends around this body of mass in what appears to be a perfect circle.