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would that object remain visible there even after the black hole had evaporated billions of years later?

what happens to the object that appears to have stopped at the former event horizon?

Which is a tad paradoxical when one considers that the speed associated with the gravitational acceleration of an object near earth is observed to be greater than it is near the moon, suggesting that the acceleration of an object near a black hole will be greater than it is on earth. A greater acceleration being synonymous with higher speeds, not slower.

Forgive me if this sounds dumb as I'm new to physics.

Quote from: timey on 07/06/2017 14:12:18Which is a tad paradoxical when one considers that the speed associated with the gravitational acceleration of an object near earth is observed to be greater than it is near the moon, suggesting that the acceleration of an object near a black hole will be greater than it is on earth. A greater acceleration being synonymous with higher speeds, not slower.It depends upon which direction your vector is pointing.

- If it is a black hole similar to the one in the center of our galaxy, millions of times more massive than the Sun, they would reach the event horizon in a finite time, and intact (assuming they were able to miss the intense radiation associated with any accretion disk that might be present).

QuoteWhich is a tad paradoxical when one considers that the speed associated with the gravitational acceleration of an object near earth is observed to be greater than it is near the moon, suggesting that the acceleration of an object near a black hole will be greater than it is on earth. A greater acceleration being synonymous with higher speeds, not slower.Well the slow down in time near the Earth due to gravity is very small (around picoseconds per second). Using the equation shown below the slow down near a blackhole is very small until you're VERY close to the horizon. What happens on the Earth and moon doesn't compare to a blackhole.t'/t = √(1 - rs/r) where rs is the radius of the event horizon. This equation also models the Earth and Sun but these bodies are orders of magnitude larger than what their rs would be if they collapsed to a black hole. Even at two times the radius of the event horizon the time dilation factor t'/t = .71. Time is running at 71% the rate of a far off observer.At r = 3/2rs is the photon sphere where light orbits and nothing else could possibly loiter without using insane amounts of fuel because there are no orbits at this distance or closer. This distance is quite close to the event horizon (1/4 the diameter of the blackhole). A lot of the accretion disk of a black hole is outside of r = 2rs. The falling matter gets to relativistic speeds (>50% c) long before gravitational time dilation becomes anywhere near zero. Look how far away the event horizon is in the NASA super computer simulation of the accretion disk below....sorry, you cannot view external links. To see them, please REGISTER or LOGIN It's easy to estimate the distance of the accretion disk is about r = 3rs at the closest point for this spinning black hole. t'/t = .82 or time is running at 82% normal rate. The frame dragging of the spinning blackhole should make this time dilation even less because the accretion disk should be spinning with the frame dragging. I'm not considering the relativistic speed of the matter because that speed becoming greater only helps show that blackholes have high speed accretion disks even with their gravitational time dilation. Including this time dilation effect for 50% light-speed is t'/t = √(1 - .5^2) = .87. Multiplying the gravitational and time dilation together only gives .71 which is still nowhere near 0.

We have no way with our current theory to know what happens as an object reaches an event horizon because we can't observe it. As to doing a coordinate transformation to the perspective of an observer falling into a black hole it prove anything as this lies outside of tested domain (Unless you've got a blackhole and you want to take a one-way trip). I don't think we can say anything scientific without some form of observation. We have pictures provided by telescopes of what looks like accretion disks and relativistic jets leaving compact dark objects. Using this we're probably pretty much right all the way down to very close to the event horizon. Extremely close to the event horizon and below we really know nothing. Sure we can use GR to make an educated guess but most physicists agree the equations break down and some (like me) are very skeptical about them working in this domain.

... And that we observers can observe that an object, (be this an object free-falling towards a black hole, or superluminal jet action direction away from a black hole), can be accelerated to relativistic speeds (speeds that are held relative to our own clock) in a field where time slows down (rates of time held relative to our own clock) is somewhat paradoxical, isn't it?

But GR time dilation is also being slowed down as the object gets closer to the black hole. On the basis that we are assuming that GR time dilation is slowing time down 'in' the geometry surrounding the black hole, (as opposed to SR time dilation that is slowing time for the object itself, yet cannot be slowing the objects speed without a mathematical paradox occurring) - If the GR time dilation in the space geometry near the black hole is becoming slower this 'will' affect the rate of the acceleration of the object.

What superluminal jets? I am not aware of anything physical going faster than light speed anywhere.

I already showed that objects move at Relativistic speeds before gravitational time dilation becomes anywhere near extreme. In fact at r = 3rs time only slows down about 18% compared to a stationary far off observer. At r = 5rs gravitational time dilation only slows things down 11%. With frame dragging this can be even less. However, in these locations objects can be moving at highly relativistic speeds well in excess of 50% light speed (and crashing into other objects).

BTW how are you measuring speed and acceleration? Whose time are you using?

What superluminal jets?

Exactly. I stipulated that it 'is' the remote observers time that we are using. But if the remote observer is observing objects at speeds that are 98% of the speed of light, (see link) but is also observing, at r = 3rs, an 18% (as you suggested) reduction of 'gravitational' time dilation as a slower rate of time - then won't the gravitational time dilation be slowing the speed of objects at r = 3rs by 18%?

From certain angles, the jets emitted by black hole/quasar accretion disks can seem to be travelling faster than light.

By the way, the power source for jets from black hole/neutron star accretion disks has been a bit of a mystery. Magnetohydrodynamics is a very complex subject to model on a supercomputer.

I've heard of certain observations that look faster than light. The point I was trying to make is no one has clear evidence anything physical goes faster than light.

If we are saying that we are observing matter at say rs=3, (or rs=5), travelling at 98% of the speed of light, but we are also saying that time at rs=3 is 18% slower than the time with which we are measuring (or rs=5 is 11% slower), then what 'actual speed' is the matter really travelling at?Think second that is 18% longer at that location.Think observed motion that is (after angular and magnetic considerations are accounted for) 98% of the speed of light, at that location...

Think second that is 18% longer at that location.Think observed motion that is (after angular and magnetic considerations are accounted for) 98% of the speed of light, at that location...

Quote from: dutch on 17/06/2017 03:21:53QuoteThink second that is 18% longer at that location.Think observed motion that is (after angular and magnetic considerations are accounted for) 98% of the speed of light, at that location...I'm not sure I understand your point you're trying to make anymore.

QuoteThink second that is 18% longer at that location.Think observed motion that is (after angular and magnetic considerations are accounted for) 98% of the speed of light, at that location...I'm not sure I understand your point you're trying to make anymore.

Translating this slower time back to the observers rate of time, the motion the observer is observing must be 98% of the speed of light + 18% (at rs=3) of 98% of the speed of light.This places the motion of matter occurring at rs=3 as being over 100% of the speed of light...

A guy here at the forum called Mike Gale tried to incorporate this variable speed of light (VLS) into the Schwartzschild metric, but he ran into problems with distance and length contraction.

Where did I say the speed of light was faster than c?

The equations from the point of view of the observer at infinity below are straight out of General Relativity and derived directly from the Schwartzchild Metric. It's important to note that this is a non-local perspective and the speed of light is always measured as c 'locally'.

Gravitational time dilation does indeed slow down clocks (and everything else including light) from the perspective of the far off observer. It does not change the speed of light locally.

QuoteTranslating this slower time back to the observers rate of time, the motion the observer is observing must be 98% of the speed of light + 18% (at rs=3) of 98% of the speed of light.This places the motion of matter occurring at rs=3 as being over 100% of the speed of light...How? I'm not following this logic.

QuoteWhere did I say the speed of light was faster than c?Nowhere. Why do you think I am under the impression that you did?

So when the speed of light is always measured as c 'locally', which local's rate of time is the observer holding 299 792 458 m/s relative to? The observer observes (hypothetically) that the rate of time is occurring 18% slower at rs=3. If a second is 18% longer at rs=3, then at the local of rs=3 the speed of light will be 299 792 458 m/second that is 18% longer than the observer's length of second.

So the speed of light is the same distance traveled held relative to the time period of a second. If a second in one part of the universe, lets say rs=3 for instance, can be 18% longer, then the speed of light at rs=3 is 299 792 458m/second that is 18% longer that the speed of light at the observers location, which is 299 792 458 m/s. At both locals the speed of light travels the same distance in the time period of a second, but each local is inherent with seconds that have an 18% difference in length.

If the observer holds the speed of light relative to the time period of a second in his own local where the 'observed" motion is 98% of the speed of light, then when he takes into consideration that it is taking the matter between 18% and 11% longer to travel from rs=3 to rs=5 in that local than it is in his own local, he will realize that the matter must be travelling between 18% and 11% faster from rs=3 to rs=5 than 98% of the speed of light of his own local...If it has taken the matter longer to travel between point A and point B, then clearly the matter must be moving faster than 98% of the speed of light. The matter will be moving between 18% and 11% faster than 98% of the speed of light held relative to the time period of a second of the local of the observer.

So this special relativity velocity addition formula - is it talking about velocity related time dilation? Calculating a velocity related time dilation that affects the velocity is a catch 22. And where it is saying /c^2, this is not taking into account differing length seconds at differing GP's. Is it?

Local Lorentz Covariance means (in part) a volume surrounding any point will measure the speed of light as c using rulers and clocks defined at that point. How large this volume is depends on how much curvature there is. If I measure the speed of light in a lab on Earth I expect to measure exactly c (the lab is relatively small and the curvature is low). However, because of curvature if I measure the speed of light of a light beam passing near the Sun (and crossing much of the solar system) I would measure a value slightly different. To my rulers and clocks the light beam would curve and appear to slow down a bit depending on r (r is the distance form the center of the Sun). If you use locally defined measuring rods and clocks you always measure c (this works at all points except for singularities where curvature goes infinity in theory).

Time AND space change. If I get what you're saying it seems somewhat correct (Maybe?) but you're not including the spatial part (a Lorentz "Contraction" effect).

No, I still don't get this line of reasoning. A large amount of matter may be moving at >50% the speed of light starting at about 3rs from the event horizon in the accretion disk (again as stated before the disk should start at about this distance as orbits become unstable closer and at 1.5rs only light can orbit). Sure, there's time dilation because the matter is moving fast and it's close to a massive object.

The Penrose Process tapping into the energy stored in the angular momentum of the blackhole and magnetic fields seem to have the ability to accelerate some matter to high speeds in jets. It's interesting and very complicated but not a paradox.

The special relativistic velocity addition equation just like the constant speed of light holds exactly in GR at all points but only in a small enough volume around a point anywhere outside the event horizon (again part of Local Lorentz Covariance; it should also hold inside the event horizon everywhere but the singularity). If spacetime is flat the volume of space the velocity addition equation holds in is infinite.

The Shapiro effect.

But now you are talking about time dilation that is velocity related. What about the gravity potential time dilation at the location/s?

Is that Penrose's twister theory?

Sticking for the mo to the observation of 98% of the speed of light motion of the jet...

But spacetime is not flat. It is curved and rippled and wavy...