Does an object orbiting close to a black hole appear to orbit slower due to time dilation?

[Ray Gunn]

Given an object in a stable close just outside the event horizon of a black hole. To a distant observer, will time dilation make the orbital period appear to be longer/slower than expected by purely Newtonian mechanics?

 

[Catastrophe]

You will get better answers than this, but here is a first shot.

It depends on how close you orbit outside the event horizon. Also, on the angle at which you view the orbit. Are you in the same plane so you see the object shuttle back and forth, or do you see it from above, so that it moves in a circle?

At the event horizon, you will view the object as stationary, but outside you will get a slower view, the closer the object is to the black hole. So, you will get slowing (as viewed from above) as it orbits around the circle) or as (in the same plane) it oscillates.

It will be slower than Newtonian view.

Cat

 

[Harry Costas]

What is time dilation?
When close to a black hole, EMR VECTORS are altered giving us a relative time reading.
Time itself does not change.

 

[Unclear Engineer]

So, is the mass calculation for a black hole adjusted for the time dilation effect when using the nearby stars' observed orbital velocities? And, are the orbital velocities corrected for frame dragging due to spin of the black hole and the orbiting mass of the stars outside of the EH?

 

[Harry Costas]

Size of a black hole (without a singularity) will determine the position of the event horizon.
Core can be several solar masses to over 100 billion solar masses. The EH can be over 10,000 light years from the massive core.

 

[Unclear Engineer]

The event horizon is not a physical surface. It is just the distance at which escape velocity exceeds the speed of light any closer to whatever is inside. That does not mean that an object could not penetrate the event horizon, if the radius is big enough that it does not create tidal forces that tear the object apart. From far outside, General Relativity solutions indicate that it appears that time slows to a stop for objects that approach and reach the event horizon. But, from the object approaching the event horizon, time does not appear to be slowing down, but distances appear to be altered, compared to a non-accelerating observer who is well outside the EH.

So, what happens inside the EH? What would it look like to an observer, who, let's say, fell through an event horizon that is 13.8 billion light years in radius (as estimated from inside the EH)? I read an article (that I can't find right now) that claimed such an observer in such a situation would see what appears to be an expanding universe. But that article did not present or describe the method for solving the General Relativity equations necessary to reach that conclusion. So, it just leaves me wondering.

 

[Absolute zero]

Given an object in a stable close just outside the event horizon of a black hole. To a distant observer, will time dilation make the orbital period appear to be longer/slower than expected by purely Newtonian mechanics?

I'm going to assume you are asking what the difference between a GR and a Newtonian orbital period would be. The Newtonian equation for orbital velocity is v=(Rs×C^2/2R)^.5 and GR is v=[Rs×C^2/2(R-Rs)]^.5 . A distant observer measures the circumference of the orbit as the same in both GR and Newtonian physics. The orbital velocity is higher in GR so the orbital period is shorter/faster. The time dilation is already built into the GR equation.

 

[Dragrath]

Yes of course but one issue with regards to this slowdown is that for most applicable black holes these effects would be accompanies with other relativistic effects such as length contraction and gravitational redshift all of which are likely only significant extremely close to the black hole.

So while a slowdown would under our current understandings of physics definitely be expected to occur as the observer sees the orbiting object appear to become stationary from the perspective of an external observer the object would also be rapidly redshifted until it ceased to be visible at all and this would probably be so close to the black hole that it effectively became unobservable. I think the only way we could ever observe these effects would be through long movies constructed from regular Event Horizon Telescope observing runs. Remember that the images of M87* actually show photons of high energy light originally hard Xrays from the inner accretion disk that got trapped in orbit around the supermassive black hole and subsequently redshifted into the radio regime. Light according to quantum electrodynamics doesn't really experience time so you will not be able to really see time dilation (except in the form of redshift). For anything less energetic than hard Xrays you aren't going to be able to observe them without absolutely enormous detectors and the photon sphere observed by the EHT is well within the Innermost Stable Circular Orbit as by definition the photon sphere is the distance at which the orbital velocity is the speed of light.

Thus to observe the slowing of matter falling into a SMBH you would need to distinguish the light from that infalling matter from the glow of the accretion disk and then track the progress as that mass falls into the BH to measure how the rate of that motion changes with time. For that you might very well need a telescope the size of the solar system if not larger making it a daunting task indeed to observe. After all if you were close enough to see the actual event directly the extremely high radiation environment would easily kill you.

 

[lanzu]

if you are very close to the horizon of the blackhole,and due to the gigantic gravity around the blackhole,there time could be static,almost stopped.