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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.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?
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?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.
#17 is replying to #15. CatI am not understanding what thelastfirst 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.I am not understanding what thelastfirst 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.
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.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?
OK, I understand that for a star or other single identifiable object.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.
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.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 can only tell you how I rectified the same " quibbles",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.