Is Blackhole's Singlarity Immobile?

[daenku32]

I don know which formula it would be based upon..E=mcc or F=ma.. But with m being (practically) infinite, would that mean all energy would be in mass and none in momentum?

If it would require impossible amout of energy to accelerate 1kg to c, wouldn't it require impossibe amout of energy to accelerate 1/0 kg to 1m/s.

[Nancarrow]

A black hole's mass isn't infinite.

[daenku32]

I just figure the basic 'particle' would be. Whereas a photon is without a mass and therefore capable of c, the singularity 'particle' would be the absolute opposite.

I know the formulas I mentioned certainly do not work beyond event horizon, but particle level stuff should, right?

[Nancarrow]

I'm not sure I understand you. No, the basic particle's mass is NOT infinite. All black holes, by which I do mean the singularities (the singularity is all that there 'is' to a black hole), have a well defined finite mass.

Of course, if the singularity is a true point particle (which is the model in general relativity, but I don't know how quantum mechanics affects that), then its DENSITY is infinite, but that doesn't make its mass infinite.

Besides, uniform motion is relative! If you have a black hole at rest, and you want to make it move at 1 m/s, you just have to move yourself at 1 m/s.

[phildonnia]

"Cygnus X-1" is believed to be a black hole orbiting a star. So it's perfectly possible to accelerate a black hole using such mundane forces as gravity. I would expect F=ma to reliably represent the situation.

[Ziggurat]

I just figure the basic 'particle' would be. Whereas a photon is without a mass and therefore capable of c, the singularity 'particle' would be the absolute opposite.

Nope. As pointed out, its mass isn't infinite, only its density. Motion is also relative, so in GR, the only meaningful way of not "moving" is not accelerating relative to your space-time geodesic (the trajectory a body takes in free fall), and since that allows for falling, orbiting, etc., in the sense that I'm sure YOU mean it, black holes can and MUST be able to move.

To get more specific, suppose you've got a star in a galaxy, which is orbiting around other stars, etc., with the whole galaxy moving as well, etc. The star has some sort of trajectory it's on, which you can plot out and predict (assuming it doesn't collide with anything else). If that star collapses into a black hole, the mass doesn't change, and that black hole will continue on that same trajectory (again, assuming it doesn't hit anything, in which case a whole number of possible things could happen in response). The gravitational field FROM the black hole will be identical to the star's at large distances, too.

[daenku32]

Nope. As pointed out, its mass isn't infinite, only its density. Motion is also relative, so in GR, the only meaningful way of not "moving" is not accelerating relative to your space-time geodesic (the trajectory a body takes in free fall), and since that allows for falling, orbiting, etc., in the sense that I'm sure YOU mean it, black holes can and MUST be able to move.

To get more specific, suppose you've got a star in a galaxy, which is orbiting around other stars, etc., with the whole galaxy moving as well, etc. The star has some sort of trajectory it's on, which you can plot out and predict (assuming it doesn't collide with anything else). If that star collapses into a black hole, the mass doesn't change, and that black hole will continue on that same trajectory (again, assuming it doesn't hit anything, in which case a whole number of possible things could happen in response). The gravitational field FROM the black hole will be identical to the star's at large distances, too.
Ok. Like Phildonnia already mentioned a black hole circling a star, I guess that should be good enough for me..
I just imagined the mass of an physically tiny particle, and therefore the density, to act as an anchor on the space-time fabric. A tire stud digging into the ice rather just gliding over it.
And consider the small cross-section of the particle, it wouldn't be subject to more than a narrow angle of a possible energy source, needing an extremely dense collision or ejection of energy to have it actually move. Like trying to move a thin guitar string with a piece of blue cheese

[Ziggurat]

And consider the small cross-section of the particle, it wouldn't be subject to more than a narrow angle of a possible energy source, needing an extremely dense collision or ejection of energy to have it actually move. Like trying to move a thin guitar string with a piece of blue cheese

Well, keep in mind that the particle's physical size isn't always the relevant property. Electrons are essentially point-like particles, but they can't pass through matter easily, even at high energies, because they feel the electromagnetic fields of other particles even at a distance (and also push back on surrounding particles even at a distance). And since everything that crosses the event horizon gets sucked in, basically anything that "hits" the event horizon will hit the singularity. So in that sense, the relevant cross-section for "pushing" on the black hole doesn't need to be small at all, and certainly isn't point-like.

[jeffq]

daenku32, if I recall my physics correctly, it takes the same force to move (or, more accurately, change the velocity of) a black hole as it does to move an "ordinary" star of the same mass. If it took a force of Fsun to impart an acceleration X on the Sun, it would take between 7 Fsun and 13 Fsun to do the same to black hole Cygnus X-1. That, in turn, would be less than the 12-18 Fsun to accelerate Betelgeuse, which is much less dense than the Sun (and way less dense than a black hole!). Density has absolutely nothing to do with it.

I'm unclear on what you mean by the particle (singularity?) being "subject to more than a narrow angle of a possible energy source, needing an extremely dense collision or ejection of energy to have it actually move". If a black hole has a companion, that companion exerts enough gravitational force to "move" it without a collision. (So would an orbiting piece of blue cheese, but not measurably so.) Distance is only relevant based on how it affects the particular force. If you're talking about hitting a black hole like a billiard ball in order to move it, I haven't thought about the implications of what would happen to your cosmic cue ball, but its momentum (mass times velocity) would be transferred to the singularity, so it would "move", regardless of whether the cue ball were Betelgeuse- or blue-cheese-sized. All that matters is that the black hole has a finite mass, and therefore cannot "resist" any force.

[Simon Bridge]

partical = singularity? Are we talking about a back hole so massive that it's gravitational attraction is large enough to overcome the Pauli repulsion?

Now bear in mind, the event horizon is not a magical point of no return. It is the distance from the center where the escape velocity is faster than light. You'll never hit it. You'll never cross it. It isn't a giant vaccuum-cleaner nozzle sucking up careless spacemen. (Mind you, from your POV - you can cross it - in principle - only there's no barrier or anything there, just you falling and the universe dying behind you.)

Black holes can interact gravitationally.
Gravitational feild is a long-range field. So, though the singularity has zero size, it also has a long long reach.

In general, physicists consider the "size" of something to be given by it's "crossection" for a given interaction. Sizes can vary a lot depending on what interaction your talking about.

The reason for this is because many things (electrons, neutrinos, singularities) don't actually have a sensible definition of physical size. All that matters is "can I hit it?"

[Molinaro]

To consider the black hole as a point like particle seems to indicate a consideration or analysis of it's size from without. However, the completion of the collapse to form that infinitely small point takes an infinite amount of time, from the point of view of everything outside the black hole.

Hence, it can never be that the black hole is infinitely small from the point of view of anyone or anything outside.. since an infinite amount of time would never have yet passed.

[Simon Bridge]

Hmmm there's a gap in my understanding of Black Holes here.
I'm not clear about how the even horizon forms in the first place, time dilation would be pretty extreme as you got so close to that transition to hole. It's bad enough near neutron stars.

he physics I have pretty much follows the formation from the collapsing stars POV - then deals with the consequences that you've got one.

Have you seen this: http://www.rialian.com/rnboyd/blackhole-dispute.htm
maybe this could be a different thread?

Anyway...

I'd imagine that one would not actually see a Black Hole as a black hole either - you'd see the neutron gas falling around it, which could be pretty hot...

However, I admit that my grasp of the extreme curvy part of general relativity is somewhat shaky.

[Ziggurat]

Hmmm there's a gap in my understanding of Black Holes here. I'm not clear about how the even horizon forms in the first place, time dilation would be pretty extreme as you got so close to that transition to hole. It's bad enough near neutron stars.
Well, let's look at the Schwarzschild metric. First, we define the Schwarzschild radius:

r_g = \frac{2GM}{c^2}

where M is the mass of the black hole. This is just to simplify the expression of the metric itself, which is:

ds^2 = \frac{1}{1 - r_g/r}dr^2 + r^2(d \theta ^2 + \sin^2 \theta d\phi ^2) - (1 - r_g/r)c^2 dt^2

When r >> r_g, then this reduces to the standard Minkowski flat space-time metric of special relativity (as we should expect). But notice what happens when we get to r < r_g: the sign of the dr term and the dt term reverse. This means that in Schwarzschild coordinates, inside the event horizon, r parameterizes TIME, not distance, and t parameterizes distance, not time. In one sense, gravitational time dilation gets so bad that time flips sideways. Falling into the black hole is no longer a question of which way in space you travel, but the inexhorable march forward of time. The sigularity is the future for everything inside the event horizon, and that's why it's inescapable. Looking at that metric, we might naively think that because the dr and dt terms go to zero AT r = r_g (the event horizon), that time stops at the event horizon and so nothing actually falls in. But this is only a coordinate singularity, not a true singularity (meaning we can find coordinates in which nothing strange happens at the event horizon). Two other coordinate systems often used for this same solution are Eddington-Finkelstein coordinates and Kruskal-Szekeres coordinates. The former are much more intuitive to picture, but the basic gist is that infalling trajectories do indeed hit the singularity in finite amount of proper time (meaning their own time). Here's a nice page on different coordinates for the Schwarzschild black hole:
http://casa.colorado.edu/~ajsh/schwp.html