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    B Perihelion shift of orbit of Mercury according to General Relativity

    Ok, I see. That actually seems cleaner, albeit more complicated. In a final attempt to wrap my head around this, is it safe to say that the velocity of an object has an impact on the geometry of spacetime relative to itself and nearby objects? An example would be a comet traveling at two...
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    B Perihelion shift of orbit of Mercury according to General Relativity

    I hope I am not taking your explanation out of context here. I cannot help but think of Special Relativity when I read this. Is the reason that the speed of the object changes the gravitational field is because the object's mass increases due to it's approaching the speed of light? The speed...
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    B Perihelion shift of orbit of Mercury according to General Relativity

    https://physics.stackexchange.com/a/26410 The second answer down the page. He mentions an explanation at the end.
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    B Perihelion shift of orbit of Mercury according to General Relativity

    So, if I'm to understand the exercise in the above example, the reason the perihelion is shifting is due to geometry? By "creating a cone like bump" somehow the elliptical-like orbital path is shifting slightly as it goes around, similar to the small lost segment of the circle that is being...
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    B Perihelion shift of orbit of Mercury according to General Relativity

    Recently, when reading an entry about Mercury's perihelion shift, someone mentioned a "hand-wavy" explanation as to why GR predicts the orbit so precisely. I was wondering if there was some elementary way to expound on what he was saying. Fundamentally, the comment said something to the effect...
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    I Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance

    Thank you for the indepth analysis and discussion, it is much appreciated. Is it possible to interpret all of the rest mass energy as sourcing from the BH's mass itself, as opposed to the object being lowered? Does this change the math? I'm assuming you can't do this, and the energy is coming...
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    I Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance

    Is it possible that the force appears to be weaker to the outside observer? Perhaps the acceleration is quicker? I'm referring directly to the experiment that determines the apparent mass of the ball.
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    I Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance

    It's a little off topic from the original post. It's buried a ways down there, but it really made an impression on me and I'm trying to get a better understanding of what it means.
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    I Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance

    https://www.physicsforums.com/threads/the-release-of-potential-energy-between-two-black-holes-goes-to-infinity-as-they-collide.972615/ Entry #24
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    I Measuring the mass of an object near the event horizon of a black hole and observing the results at a distance

    In a recent thread we discussed the idea that an object slowly dropped into a black hole, can have its rest mass recovered, as energy, if slowly brought to a halt at the event horizon. Once the object is dropped, it would be unrecoverable, and the BH would gain no new mass. I am under the...
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    I Is it possible to reduce or modify Einstein's Field Equations so they exactly mirror Newtonian gravity behavior?

    For this discussion, I mean exact. I am more interested in the mathematical mechanics than the measurability or accuracy. In fact, I would expect Newton's equation to fall out of the math, and I guess that's what I was kind of driving at. Trying to understand if there is some way to modify...
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    I Is it possible to reduce or modify Einstein's Field Equations so they exactly mirror Newtonian gravity behavior?

    Would an example of a changing field be something like two large bodies passing close to one another, or a body spinning?
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    I Is it possible to reduce or modify Einstein's Field Equations so they exactly mirror Newtonian gravity behavior?

    Is it possible to reduce and/or modify the EFE so that they make the exact same prediction as Newton's law of gravity? I am wondering if the slight differences in prediction from these two mathematical approaches can be identified at a particular place in the EFE or if it's the geometrical...
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    I The association of energy, pressure, mass, etc. with the four dimensions in Einstein's Field Equations

    If I am understanding correctly, each of these time-space or time-time (I think there are 10 combinations), all have an equivalent physical description that can be identified, for example mass, or momentum, pressure, etc. and these identifications are then desribed on the right hand side of the...
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    I The association of energy, pressure, mass, etc. with the four dimensions in Einstein's Field Equations

    While viewing a recent lecture on Einstein’s Field Equations, the presenter made the association between the various quantities like mass, energy, momentum and pressure directly to the four dimensions of spacetime. Depending on which derivation of the FE he was explaining, he would make an...
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    I Can empty space be considered ‘elastic’ and expandable?

    Ok, please allow me a final attempt to bend my mind around this and I'll go. By defining metric spaces (like the ones that make vaccuum appear to expand), these are just dynamic (or curved space-time like) coordinate systems, and we can just as easily apply a non-expanding or even a contracting...
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    I Can empty space be considered ‘elastic’ and expandable?

    I guess what I'm hoping to understand is if the metric expansion of space itself is somehow energy dependent in a way that is different from normal relative velocities of objects (like in an explosion). I thought by framing the question in a vacuum, and then populating the vaccuum with matter...
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    I Can empty space be considered ‘elastic’ and expandable?

    When you say it is no longer meangingful, is that because it is empty space? In a universe like ours, when matter is being separated, things must have some kind of momentum or energy to drive them apart? I'm trying to imagine how this applies to what we see and if we can place any significance...
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    I Can empty space be considered ‘elastic’ and expandable?

    When we speak of expansion in this way, does the expansion of a vaccuum require energy input to get it going, even without matter? Admitedly, this is a little above my head. Does anyone have any introductory reading that can help? (I hope it is appropriate to ask for recommendations on this site)
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    I Can empty space be considered ‘elastic’ and expandable?

    The intention of this question is to get to the heart of the geometrical properties of space-time according to GR, and to focus entirely on what the theory allows, and not so much on what we actually see. I would like to consider a perfect vacuum, in a euclidian infinite void, completely devoid...
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    I Can an object fall into a black hole at faster that the speed of light?

    Thank you for the answers and discussion! I will post my follow up question as a separate thread, as I think it belongs in a new post.
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    I Can an object fall into a black hole at faster that the speed of light?

    If I may press a little further, if I am a telescope observer with the right equipment, I observer a galaxy that is very far, far enough to have a redshit that implies a recession velocity that is significantly higher than c (in step with normal cosmological expansion). Perhaps this redshift...
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    I Can an object fall into a black hole at faster that the speed of light?

    So, to clarify, is it correct to say that local objects never have a relative velocity from one another above c, and I also imagine a distant region, which also has local objects confined to c, but that these two distant regions appear to be receding faster than c. So, is it then impossible for...
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    I Can an object fall into a black hole at faster that the speed of light?

    I am wondering if an object can fall into a blackhole at faster that the speed of light. I have heard that the expansion of the universe can make distant galaxies appear to recede from one another at velocities faster than the speed of light.

 Intuitively, this makes sense to me. I am...
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    Defining negative energy of gravitational field

    Just out of curiosity; when you say that a field has momentum and angular momentum, does that mean if they spin, then somehow the field will want to continue spinning momentarily if the source of the field is suddenly stopped from spinning? Or does that mean the field has angular momentum in...
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    Defining negative energy of gravitational field

    Ok, so the energy/mass is the energy of the field itself. This sounds familiar, I remember something about the energy of gravity itself adding to the gravitational field in GR, in a kind cascading effect that should be taken into account. But this sounds to me like the energy is positive and...
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    Defining negative energy of gravitational field

    I think this outlines part of the confusion I've been having. I was under the impression that gravity according to GR wasn't really a force acting on objects at all, but instead, objects simply coasting along warped geodesics, and experiencing no force of acceleration. To me this sounds like...
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    Defining negative energy of gravitational field

    I have been learning that gravity has a negative energy associated with it. I've heard this stated a couple different ways, but I would like to understand a distinction. One line of thought declares that the potential energy of an object within a gravitational field is negative. Another line...
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