# Gravitational waves and others contradictoriness

1. Jul 1, 2012

### Dinar

Can anybody explain me those contradictions.
1.If gravitation has speed = c and spread in form of gravitation wave. How it can escape Schwarzschild radius in black hole?
2. Magnetic field for black hole - how it can be possible? What create magnetic field?
3. Electrically charged black hole - the same as first one - How electrical field can escape?
4. Rotating black hole. Formula for time:

The equation is:

t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}} , where

t_0 is the proper time between events A and B for a slow-ticking observer within the gravitational field,
t_f is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate),
G is the gravitational constant,
M is the mass of the object creating the gravitational field,
r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),
c is the speed of light, and
r_0 = 2GM/c^2 is the Schwarzschild radius of M.

What speed random point on Schwarzschild radius should have for observer outside of black hole to see any movement of it?

Last edited: Jul 1, 2012
2. Jul 1, 2012

### Drakkith

Staff Emeritus
The wave is in the metric of spacetime itself. The metric is not a physical object attracted by gravity. In an analogy, if spacetime was like a rubber sheet, and a black hole was a bowling ball placed on it, it would be like asking how the rubber sheet isn't sucked up into the black hole.

3. Jul 1, 2012

### Q-reeus

I rarely visit this section but your thread caught my eye. A non-expert's opinion:

1: GW's (gravitational waves) are generated by motions of matter exterior to any EH (event horizon). In the standard GR view where BH's (black holes) make sense, a portion of the generated GW's are swallowed inside of EH, but remainder can always escape.
2: Magnetic field is similarly generated exterior to EH - inswirling ionized gas creates circulating currents. Much more on that here: https://www.physicsforums.com/showthread.php?t=595261
3: That's a good one. You might have already looked at this by now lengthy and unfortunately fragmented thread that has simply petered out: https://www.physicsforums.com/showthread.php?t=612091
4: Again in standard view where entity 'BH' exists, there is a Kerr solution that has spacetime being 'dragged around' with the spinning BH, and it's only motion relative to that dragged frame, at the EH, that would be paradoxical. Also, given that anything at the EH must be infalling and have infinite redshift wrt an external observer, said external observer cannot in principle observe a 'random point' there, and could only infer a rotational speed relative to distant observer. This article may help: http://www.cosmosmagazine.com/node/873 [Broken]

Last edited by a moderator: May 6, 2017
4. Jul 1, 2012

### Chronos

See http://curious.astro.cornell.edu/question.php?number=264 [Broken].

Last edited by a moderator: May 6, 2017
5. Jul 1, 2012

### Naty1

You have one idea right: that nothing escapes from inside a black hole untilit eventually collapses of it's own accord after it slowly radiates away.

But none these entities were ever 'inside' the black hole and therefore did not need to escape...the horizon forms and these characteristics remain outside the BH horizon. Think of a charge sitting on the outside of a conducting sphere. Another way to say the same thing is that these characteristics are from the past lightcone of the material/charge/matter whatever it was that formed the black hole. If new matter or charge drops inside, you can view that information as being smeared across the existing horizon....it's analogous to ADS/CFT correspondence....everything inside appears outside on the surface horizon.

In Schwarzschild coordinates it takes an infinite coordinate time for anything to cross the horizon, even though physically it only takes a finite proper time for a falling object to cross the horizon. Inside the horizon, Schwarzschild coordinates reverse the role of time and space--the radial coordinate in Schwarzschild coordinates is physically spacelike outside the horizon but timelike inside, while the time coordinate in Schwarzschild coordinates is physically timelike outside the horizon but spacelike inside. Another view appears in Kruskal-Szekeres coordinates where in contrast objects crossing the horizon will cross it in a finite coordinate time, and the Kruskal-Szekeres time coordinate is always timelike while its radial coordinate is always spacelike.

So when you read descriptions you have to note which coordinates are used and explanations are sometimes coordinate dependent meaning they do not represent local [physical] observables.

6. Jul 1, 2012

### Q-reeus

Why do I get the distinct impression this is targetting just point 3: in my reply in #3? Maybe a complete mistake, but either way, may I extend to Chronos an invitation. Please - if that link you supplied makes complete sense, and you are fully cognisant of all ramifications therein, please enter the 'unfortunately stalled' discussion at https://www.physicsforums.com/showthread.php?t=612091
and supply your own completely consistent resolution. No offense and obligation of course, but excuse me for drawing certain conclusions if the invite is not taken up! Not that I'm suggesting Astrophysics section is a relative backwater, but in SR/GR, the thread count does tend to be somewhat brisker.

Last edited by a moderator: May 6, 2017
7. Jul 1, 2012

### Dinar

Talking space-time I didn't find any equation for space change in gravitational field, but if EH infalling and have infinite redshift wrt for external observer equation for space should be the same as for time ΔS = ΔS°√1-r°/r and for EH →0. It means that for observer inside EH space shrink to one point and time stopes. So EH is one point of space warped around BH. Then what is rotating?

Last edited by a moderator: May 6, 2017
8. Jul 1, 2012

### Chronos

This excerpt from the referenced article sums it up -
"In the quantum universe, forces are mediated by virtual bosons, like photons and gravitons. ... Virtual particles are essentially allowed to do anything at all short of violating causality during their lifetimes."
This explanation applies to gravity, magnetic and electric fields. Other characterizations are used to convey a more classical sense - like Matt McIrvin's 'fossil field' explanation at http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html
"... If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole. Just as the light registering late stages in my fall takes longer and longer to get out to you at a large distance, the gravitational consequences of events late in the star's collapse take longer and longer to ripple out to the world at large. In this sense the black hole is a kind of "frozen star": the gravitational field is a fossil field. The same is true of the electromagnetic field that a black hole may possess."

9. Jul 1, 2012

### Q-reeus

English is probably not your first language Dinar - which may explain why I'm having trouble following your post. Best I can tell, you are saying that for a locally infalling 'astronaut' everything seems to comes to a crashing stop at EH. Not so in standard GR picture - there are many discussions in SR/GR section and maybe here that will reconcile 'time freezing and radial length shrinkage to zero' as artifacts of using Schwarzschild coordinates. Transform to another coordinate scheme such as Kruskal–Szekeres coordinates and that particular problem is 'solved'. Personally, I'm not impressed, but that will be considersd an uninformed 'maverick' viewpoint. Point of my #3 was one needs to be very careful about identifying 'anomalies' - most (many will say all) are simple misidentification of physical connections. In my view that includes all your points in #1 except 3: which imo is genuine, but to get to that position requires persuing a lengthy process of elimination.

10. Jul 1, 2012

### Q-reeus

Funny but I got from that same source [oops - actually, following source] "In addition, however, virtual particles aren't confined to the interiors of light cones: they can go faster than light!" What is the definition of causality again?
Formally I can agree with the gravitational part. That's because gravitational redshift of infalling matter (coordinate perspective) is exactly balanced by rising KE of infalling matter. It imo progressively becomes though a precarious balancing act where rapidly from external perspective one arbitrarily approaches infinity x zero = 'what you want' = 'fossil gravitational field'. I strongly dispute the same precarious balancing act can at all apply to infalling charge - charge does not 'grow' like the locally observed infalling KE of mass does. There is (locally) observed charge invariance but *not* gravitating mass invariance! But this is apparently flogging a dead horse, so best for peace of mind to accept concordance viewpoint.

Last edited: Jul 1, 2012