# 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

##### "Science begets knowledge, opinion ignorance.
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.

billslugg

#### 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.

#### Absolute zero

Yes for the observer near the black hole, his clock runs slower than the distant observer's clock. The distant observer's clock is unaffected and his observations of the object's velocity near the black hole is unaffected too.

I think a thread on the deference between what is observed and what is seen maybe appropriate.

Catastrophe

#### Unclear Engineer

According to General Relativity, the clock of an observer runs slower when it is closer to a large gravitational object. The difference in time passed on 2 clocks at different altitudes is not lost by moving the two clocks to the same altitude, so the difference in clock elapsed times can be compared by truly simultaneous observations in the same place at the same time at zero relative speed.

On the other hand, to an observer far "above" an object orbiting a black hole, the apparent velocity of something in orbit should also be obeying the Lorentz Transformations, making things look different when the object is heading toward or away from the distant observer, but not when heading along the part of the orbit perpendicular to the line of sight.

So, I am not sure what to expect as astronomers try to determine things about a black hole, such as mass and spin, by looking at things like red shifts and transit times of orbiting objects. I think those 2 methods, when developed, would appear to give conflicting results unless both types of effects are properly accounted for.

A third effect that probably needs to be quantitatively accounted for is "frame dragging", where the rotation/spin of the black hole drags space itself into a spiral near the black hole.

Actually doing this type of mathematical correction adjustment is above my pay grade, beyond my education, and maybe even beyond my maximum mental capabilities.

#### Absolute zero

What an observer 'sees' depends on location, location and location. With a black hole, locations can be described in a way to make it clear what is being seen. For example: distant observer (D) is looking at a black hole from a position perpendicular to the orbital plane of observer B. Stationary and close to the orbital plane of B is observer A. B is in orbit at R=2Rs. A's clock will run ~.7 times slower than D's clock. B's clock will run ~.7 times slower than A's clock. D's observation of the orbital period of B is unaffected by the slowing of A's or B's clock. Gravitational lensing will cause D to see the orbit of B to be larger than calculated but the orbital period is unaffected. Gravitational lensing will make the apparent velocity of B to be larger than calculated by D.

Catastrophe

#### Unclear Engineer

What an observer 'sees' depends on location, location and location. With a black hole, locations can be described in a way to make it clear what is being seen. For example: distant observer (D) is looking at a black hole from a position perpendicular to the orbital plane of observer B. Stationary and close to the orbital plane of B is observer A. B is in orbit at R=2Rs. A's clock will run ~.7 times slower than D's clock. B's clock will run ~.7 times slower than A's clock. D's observation of the orbital period of B is unaffected by the slowing of A's or B's clock. Gravitational lensing will cause D to see the orbit of B to be larger than calculated but the orbital period is unaffected. Gravitational lensing will make the apparent velocity of B to be larger than calculated by D.

So, if we are lucky enough to be roughly in the position of this observer A for some distant galaxy, we would see a star that is really at twice the event horizon distance orbiting with the correct period for that distance, but the wrong distance (orbital diameter), and say that the velocity of the star was higher than it should be if we actually know the mass of the black hole. Or, if we do not know the mass of the black hole, we would think that its mass is greater than it really is because we measure the orbital velocity to be higher than we would expect at the distance observed for the correct mass. Right?

Now, what is the effect of frame dragging on these observations, as a function of the spin of the black hole?

Assuming that astronomers are making all of these adjustments, I still wonder how they somehow independently know the black hole mass and spin, and the actual diameters of observable orbits.

And, for Sagittarius A*, were we observers are more or less in the plane of the orbits, but not so close as observer A, it seems that we need to deal with Special Relativity effects to get a measure of star orbit velocities by red/blue shifts, as well as deal with gravitational lensing and frame dragging.

Absolute zero

#### Absolute zero

Observer A and B are 2Rs from the center of the black hole.
If the black hole has an Rs of 10km than 2Rs is 20km.

Every black hole we observe from earth, we are the distant observer. Our clock is unaffected by objects we observe. Try to figure out what you would see in different situations in special relativity before tackling GR. What would you see when observing an object with a velocity of .99c moving away or moving toward earth. Does the rate of time the observed object effect the velocity we observe?

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Catastrophe

#### Harry Costas

OK
Can someone define a Black Hole or give an opinion if possible?

#### Harry Costas

If your clock is not affected by gravity or electromagnetic vector fields then time reading is not affected.
Time is not an item that changes.
Y
The clock is the thing that changes in showing time.

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
Here is informatiom on black holes.

Black hole - Wikipedia
https://en.wikipedia.org › wiki › Black_hole

A black hole is a region of spacetime where gravity is so strong that nothing – no particles or even electromagnetic radiation such as light – can escape ...
List · ‎Outline of black holes · ‎Black hole (disambiguation)

Absolute zero

#### Unclear Engineer

I am not understanding what the last first 3 of the last 4 posts are trying to get at.

We are always distant observers for any black hole, at least until we learn how to travel 27,000 light years from earth. So, what matters is our line of sight relative to the plane of the orbit of a star close to a black hole, and to the axis of spin of the black hole, which may not be completely identical, but should be similar.

Special Relativity effects should alter our perceptions of motions that are coming toward us or going away from us, which would be the situation when we view an orbital plane edge-on and the orbiting body is in a position that beings it toward us or away from us at relativistic speed - which is a large part of the orbit when you look at the cosine of its velocity vector for its path relative to the line of sight to us here on Earth.

So, my question was regarding how that would affect red shift measurements made here on Earth when we try to use them to measure the mass of the black hole. Other issues that would also affect the use of red shifts include the gravitational red shift and the gravitational lensing affecting size measurements. And, apparent rotational period would be affected by frame dragging, too, right?

So, with that many perception-altering effects and only a few measurements to adjust and work with to deduce the mass and spin of a black hole, how are we sure we have done that correctly?

I would think that it might be possible to look at the orbits of multiple close-in stars and do a best-fit analysis. But, then I remember that it was the apparent lack of fit for stars orbiting father from the black holes that led to the introduction of "dark matter", whose distribution we must also deduce from the motions of stars. So, I am wondering if we really have enough measurements to pin down all of the parameters to a unique solution, at least without making some "simplifying assumptions" that may be misleading us.

I am not understanding why Harry Costas is asking for a definition of a "black hole". Harry, what are you asking for besides "a region of space from which light cannot escape because the mass within it causes the escape velocity to exceed the speed of light"? It seems to me that definition is sufficient for observers here on Earth.

I have some quibbles about what it means for an observer near the event horizon. For instance, light emitted "outward" from an object orbiting just inside the event horizon should have its frequency reduced to zero as that light travels to some distance above the event horizon, rather than hitting a brick wall at that boundary, right? At least for physical particles with mass, the acceleration of gravity takes some time to turn an "upward"-bound mass velocity into a downward velocity, during which period the particle travels upward some distance.

But, considering we are talking about light, and passage of time near and maybe even slightly inside an event horizon, I am not sure how to think about it. And, I am not confident that, if we could actually go there and make measurements, we wouldn't find yet anther "paradox" like the double-slit experiment that shows we really don't understand as well as we think we do.

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
I am not understanding what the last first 3 of the last 4 posts are trying to get at.

We are always distant observers for any black hole, at least until we learn how to travel 27,000 light years from earth. So, what matters is our line of sight relative to the plane of the orbit of a star close to a black hole, and to the axis of spin of the black hole, which may not be completely identical, but should be similar.

Special Relativity effects should alter our perceptions of motions that are coming toward us or going away from us, which would be the situation when we view an orbital plane edge-on and the orbiting body is in a position that beings it toward us or away from us at relativistic speed - which is a large part of the orbit when you look at the cosine of its velocity vector for its path relative to the line of sight to us here on Earth.

So, my question was regarding how that would affect red shift measurements made here on Earth when we try to use them to measure the mass of the black hole. Other issues that would also affect the use of red shifts include the gravitational red shift and the gravitational lensing affecting size measurements. And, apparent rotational period would be affected by frame dragging, too, right?

So, with that many perception-altering effects and only a few measurements to adjust and work with to deduce the mass and spin of a black hole, how are we sure we have done that correctly?

I would think that it might be possible to look at the orbits of multiple close-in stars and do a best-fit analysis. But, then I remember that it was the apparent lack of fit for stars orbiting father from the black holes that led to the introduction of "dark matter", whose distribution we must also deduce from the motions of stars. So, I am wondering if we really have enough measurements to pin down all of the parameters to a unique solution, at least without making some "simplifying assumptions" that may be misleading us.

I am not understanding why Harry Costas is asking for a definition of a "black hole". Harry, what are you asking for besides "a region of space from which light cannot escape because the mass within it causes the escape velocity to exceed the speed of light"? It seems to me that definition is sufficient for observers here on Earth.

I have some quibbles about what it means for an observer near the event horizon. For instance, light emitted "outward" from an object orbiting just inside the event horizon should have its frequency reduced to zero as that light travels to some distance above the event horizon, rather than hitting a brick wall at that boundary, right? At least for physical particles with mass, the acceleration of gravity takes some time to turn an "upward"-bound mass velocity into a downward velocity, during which period the particle travels upward some distance.

But, considering we are talking about light, and passage of time near and maybe even slightly inside an event horizon, I am not sure how to think about it. And, I am not confident that, if we could actually go there and make measurements, we wouldn't find yet anther "paradox" like the double-slit experiment that shows we really don't understand as well as we think we do.
#17 is replying to #15. Cat

Absolute zero

#### Absolute zero

I am not understanding what the last first 3 of the last 4 posts are trying to get at.

We are always distant observers for any black hole, at least until we learn how to travel 27,000 light years from earth. So, what matters is our line of sight relative to the plane of the orbit of a star close to a black hole, and to the axis of spin of the black hole, which may not be completely identical, but should be similar.

Special Relativity effects should alter our perceptions of motions that are coming toward us or going away from us, which would be the situation when we view an orbital plane edge-on and the orbiting body is in a position that beings it toward us or away from us at relativistic speed - which is a large part of the orbit when you look at the cosine of its velocity vector for its path relative to the line of sight to us here on Earth.

So, my question was regarding how that would affect red shift measurements made here on Earth when we try to use them to measure the mass of the black hole. Other issues that would also affect the use of red shifts include the gravitational red shift and the gravitational lensing affecting size measurements. And, apparent rotational period would be affected by frame dragging, too, right?

So, with that many perception-altering effects and only a few measurements to adjust and work with to deduce the mass and spin of a black hole, how are we sure we have done that correctly?

I would think that it might be possible to look at the orbits of multiple close-in stars and do a best-fit analysis. But, then I remember that it was the apparent lack of fit for stars orbiting father from the black holes that led to the introduction of "dark matter", whose distribution we must also deduce from the motions of stars. So, I am wondering if we really have enough measurements to pin down all of the parameters to a unique solution, at least without making some "simplifying assumptions" that may be misleading us.

I am not understanding why Harry Costas is asking for a definition of a "black hole". Harry, what are you asking for besides "a region of space from which light cannot escape because the mass within it causes the escape velocity to exceed the speed of light"? It seems to me that definition is sufficient for observers here on Earth.

I have some quibbles about what it means for an observer near the event horizon. For instance, light emitted "outward" from an object orbiting just inside the event horizon should have its frequency reduced to zero as that light travels to some distance above the event horizon, rather than hitting a brick wall at that boundary, right? At least for physical particles with mass, the acceleration of gravity takes some time to turn an "upward"-bound mass velocity into a downward velocity, during which period the particle travels upward some distance.

But, considering we are talking about light, and passage of time near and maybe even slightly inside an event horizon, I am not sure how to think about it. And, I am not confident that, if we could actually go there and make measurements, we wouldn't find yet anther "paradox" like the double-slit experiment that shows we really don't understand as well as we think we do.

I am trying to keep my posts relevant to the OP's question.

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?

Short answer, no. Time dilation there isn't a factor here. GR has a shorter/faster orbital period than Newtonian mechanics.

Catastrophe

#### Absolute zero

Special Relativity effects should alter our perceptions of motions that are coming toward us or going away from us, which would be the situation when we view an orbital plane edge-on and the orbiting body is in a position that beings it toward us or away from us at relativistic speed - which is a large part of the orbit when you look at the cosine of its velocity vector for its path relative to the line of sight to us here on Earth.

So, my question was regarding how that would affect red shift measurements made here on Earth when we try to use them to measure the mass of the black hole. Other issues that would also affect the use of red shifts include the gravitational red shift and the gravitational lensing affecting size measurements. And, apparent rotational period would be affected by frame dragging, too, right?

None of the following is to be taken as gospel, how I would try to unravel this is to take measurements of the maximum red shift of object orbiting the black hole. Than convert it to a velocity. Do the same for the minimum red shift (or blue shift, depending on the situation). From this, orbital velocity can be calculated. From orbital velocity, the R value of the orbit is calculated. With the R value, the Gravitational red shift can be calculated and applied to the original orbital doppler shifts. If the doppler shifts balance (velocity away equals velocity twards) than black hole is not rotating. If the black hole is spinning, cancel out the reference dragging until the doppler shifts balance.

Unclear Engineer

#### Unclear Engineer

None of the following is to be taken as gospel, how I would try to unravel this is to take measurements of the maximum red shift of object orbiting the black hole. Than convert it to a velocity. Do the same for the minimum red shift (or blue shift, depending on the situation). From this, orbital velocity can be calculated. From orbital velocity, the R value of the orbit is calculated. With the R value, the Gravitational red shift can be calculated and applied to the original orbital doppler shifts. If the doppler shifts balance (velocity away equals velocity twards) than black hole is not rotating. If the black hole is spinning, cancel out the reference dragging until the doppler shifts balance.

OK, I understand that for a star or other single identifiable object.

But, if you do that for more than one star, at substantially different R values, don't you get conflicting results that are then reconciled by assumptions about dark matter?

I do not know what is really happening with the results of calculations like that, so I am only asking, based on what I have read on the Internet - and we know how reliable that is.

#### Absolute zero

OK, I understand that for a star or other single identifiable object.

But, if you do that for more than one star, at substantially different R values, don't you get conflicting results that are then reconciled by assumptions about dark matter?

I do not know what is really happening with the results of calculations like that, so I am only asking, based on what I have read on the Internet - and we know how reliable that is.

I don't know, substantially different R values covers a pretty big volume and possible situations. But for any value of R where Gravitational red shift would be significant, I can't imagine dark matter would be a significant factor.

What we really don't know is if I know anything

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#### Absolute zero

I have some quibbles about what it means for an observer near the event horizon. For instance, light emitted "outward" from an object orbiting just inside the event horizon should have its frequency reduced to zero as that light travels to some distance above the event horizon, rather than hitting a brick wall at that boundary, right? At least for physical particles with mass, the acceleration of gravity takes some time to turn an "upward"-bound mass velocity into a downward velocity, during which period the particle travels upward some distance.

I can only tell you how I rectified the same " quibbles",

First, try to forget about Newtonian gravity and replace it with spacetime warping. The spacetime at the event horizon is so warped that time doesn't exist (question is 'does spacetime exist without time'). Light cannot originate from inside the event horizon. (Escape velocity is greater than C) For light originating just outside the event horizon, the only paths out to the rest of the universe are neatly straight up. All other paths, the curvature of spacetime returns the light to the event horizon.

Any further explanation requires getting into gravitational redshift with out using Newtonian physics. If interested, just ask and I'll stir up the mud.

#### Catastrophe

##### "Science begets knowledge, opinion ignorance.
Absolute Zero
"question is 'does spacetime exist without time'"

Is it too simplistic, in spacetime coordinates, to have x, y, z, t = constant?
Or if you have 4-dimensional graph, simply ignore t axis?
You have ignored time, you are without time, but simply existing in the 3-space dimensions - without denying the existence of the 4th time dimension. <sup>

Cat

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