The event horizon isn't an object.Paige_Turner said:
Gravitational time dilation in general is not a particularly useful concept in GR. If two black holes collide and merge, then there is a much more complex spacetime and time dilation is not really well defined.Paige_Turner said:
No, but you may be misunderstanding what it means here.Paige_Turner said:
Ok. But isn't the sloppiness that you say the Doppler shift here reduces the frequency (red/blue) but not the frequency (of strobe pulses)? Light is always c.Nugatory said:
Doppler affects both the spacing between the flashes and the frequency of the light within each flash. When the source and the receiver are moving apart each successive flash has to travel a longer distance than its predecessor, so spends a bit longer in flight.Paige_Turner said:
Imagine I shine two identical lasers at you. One I leave continuous and the other I block and un-block for 1,000 wave cycles each time. If the frequency you receive is lower than the one I emit then the 1,000 cycle pulses must be lengthened. Also the gaps must be longer, since you need to receive 1,000 cycles of the red shifted continuous laser in the gap between the pulses.Paige_Turner said:
My try for still minimizing sloppiness: To identify "purely" gravitational time dilation would require to measure the elapsed time of a clock stationary close to the black hole (eventually by means of a long rope for bringing the clock down and up again for comparison with our clock and thereby neglecting the elapsed time for this).Nugatory said:
That sounds like "slow clock transport". It is one way to synchronize clocks at a distance (as long as you can hold those clocks "stationary"). Unless my intuition is failing me badly, it is a method that coincides with Schwarzschild coordinates.timmdeeg said:
You don't have to do anything so complex with the ropes. You can just have clocks at fixed altitudes use radar to confirm that they are in a fixed altitude relationship and simply watch each other's clocks through telescopes. They'll find that the time dilation each one sees is the reciprocal of the time dilation the other sees.timmdeeg said:
But isn't the rate of the clock tick at constant ##r## distorted (smudged?) if we watch it with the telescope, as the light loses energy during climbing up?Ibix said:
Don't see why. And if there is some error ##\Delta t## in your timing of a tick of my clock I would not expect that error to increase with repeated pulses. So you can always time (say) 100 ticks of my clock and get an error of ##\Delta t/100## on my tick duration.timmdeeg said:Thanks @jbriggs444 and @Ibix for your comments. I must confess that regarding the rope I was influenced by Robert Geroch's "General Relativity fro A to B" where he explains several situations around Black holes with sketches showing ropes.
But isn't the rate of the clock tick at constant ##r## distorted (smudged?) if we watch it with the telescope, as the light looses energy during climbing up?
The tick rate is subject to what we could refer to as gravitational time dilation. Yes. If both sending and receiving clocks are hovering there is no "smudging". One receives a perfectly regular dilated tick rate on the high end. Or a perfectly regular increased tick rate on the bottom end.timmdeeg said:Thanks @jbriggs444 and @Ibix for your comments. I must confess that regarding the rope I was influenced by Robert Geroch's "General Relativity fro A to B" where he explains several situations around Black holes with sketches showing ropes.
But isn't the rate of the clock tick at constant ##r## distorted (smudged?) if we watch it with the telescope, as the light loses energy during climbing up?
Yes. If the ticks are light pulses then each tick arrives redshifted at the high end but that doesn't affect the tick rate. I have been misled initially by imagining the clock to be replaced by a monochromatic light source and came up wrongly with "loses energy during climbing up".jbriggs444 said:
It does affect the tick rate.timmdeeg said:
Ok let's stay with this example. Idealized now, if one could bring up this clock extremely fast it would show 2 second intervals. This tickrate (2 seconds per interval) is due to the stay at the bottom. That's what I tried to express.jbriggs444 said:
I am not following.timmdeeg said:
My fault.jbriggs444 said:
Yes.jbriggs444 said:
Yes, at the same place both clocks tick at the same rate. What I meant but didn't express unfortunately is that the clock after being brought up very fast shows less elapsed time compared with the top clock due to its stay at the bottom.jbriggs444 said:
Ok, that makes sense.timmdeeg said:
Black holes collide when their gravitational pull becomes strong enough to overcome their own inertia. This can happen when two black holes are in close proximity to each other and their orbits begin to decay, causing them to merge and form a single, larger black hole.
When black holes collide, they release a tremendous amount of energy in the form of gravitational waves. These waves ripple through space and time, carrying information about the collision and the resulting changes in the fabric of the universe.
We can observe black hole collisions by detecting the gravitational waves they produce. This is done using specialized instruments such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo interferometer. These instruments are able to detect tiny distortions in space caused by passing gravitational waves.
Currently, it is not possible to predict exactly when black holes will collide. However, scientists can make predictions based on observations of black hole pairs and their surrounding environments. As technology and our understanding of black holes advances, we may be able to make more accurate predictions in the future.
The time it takes for black holes to collide can vary greatly depending on their size, distance, and other factors. Some collisions may happen in a matter of seconds, while others may take millions or even billions of years. It also depends on our ability to detect and observe these events, as they may have already occurred in the distant past but their effects are just reaching us now.