Here's a thought experiment: Say we have a cloud of theoretical test particles (no mass, no charge) that is far, far away from anything, with none of the particles moving with respect to any of the others. Then we introduce a Schwarzschild black hole into the vicinity. My understanding is that the arrangement of the particles in the cloud would be different, with those aligned radially to the black hole now measured to be further apart while those aligned orthogonally measured to be closer together.

If I understand this correctly, none of the marker particles would have actually moved through space. It is the space itself that has changed and the apparent movement of the test particles is due to the way the spacetime manifold has been distorted by the presence of the black hole.

Assuming I haven’t gone too far off the rails so far, do the displacements described above apply as well to real, physical objects? Does it result in actual distortions of objects? For instance, is it the cause of the infamous spaghettification forces that rip things apart?

EDIT: Since there seems to be a lot of misunderstanding about what I meant by "test particles", allow me to apologize for my lack of clarity and emphasize here that these are NOT REAL PARTICLES. This whole question is a THOUGHT EXPERIMENT. The test particles are only hypothetical marker points in the coordinate system that would not change their relative positions due to gravity or charge effects between the particles, themselves.

The idea is that, due to metric stretching, the "markers" would be measured to be in different positions IF a black hole were present then they would be if the black hole were not present.

  • $\begingroup$ Related post by OP: physics.stackexchange.com/q/414963/2451 $\endgroup$ – Qmechanic Jul 3 '18 at 17:12
  • $\begingroup$ no mass and with none of the particles moving with respect to any of the others are contradictory statements. Massless particles move with the velocity of light. Only massive ones can be at rest with each other. A black hole of any kind cannot just be introduced, it is either there, or not. If it is there, it will be shaping the space time for the massive particles at rest which also are shaping space time , if it is not there the particles will be shaping space time . $\endgroup$ – anna v Jul 3 '18 at 19:30
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    $\begingroup$ @anna v ... I agree with everything you say but the operative term here is "theoretical". The question is meant to be a thought experiment. The test particles are just pure, theoretical marker points (not actual particles) in empty space. And yes, I understand you can't just add a black hole at will. Please forgive me for not explaining it more thoroughly but I have seen the format used in many other places to discuss theoretical points. I thought it was more common than it apparently is. Sorry. $\endgroup$ – dcgeorge Jul 3 '18 at 19:56
  • $\begingroup$ It is the distiction between coordinate points, which can be as you describe, but they are not "test particles". Test particles are idealizations of real particles, and coordinate points cannot represent them. "change" can only happen to physical test particles. $\endgroup$ – anna v Jul 4 '18 at 3:15
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    $\begingroup$ The attitude of being "annoyed" by constructive criticism (or just by the efforts of others to make sure the matter is very clear) is perceived as unfriendly. People here volunteer to spend time and effort helping others for no personal benefit, so the least you can do is being polite to them. $\endgroup$ – safesphere Jul 6 '18 at 20:44

If you have a cloud of test particles in the spacetime surrounding a static and spherically symmetric black hole, the corresponding neighbouring geodesics experience a relative acceleration. The acceleration is different for points separated radially or along the azimuthal coordinate. That is what explains the gravitational tidal force that applied to an extensive object causes it to stretch and rip apart, i.e. the so-called spaghettification.

However your statement:
none of the particles have actually moved through space
is not correct, as the particles do move in spacetime.

From the comments I understand you referred to the coordinates, however to think to materialize a black hole in a flat spacetime, even if conceptually, would require a time-dependent description and ask for gravitational waves to propagate the information in the spacetime around. The flat spacetime would be distorted and shaped according to the Schwarzschild metric.

  • $\begingroup$ Thanks Michele. I think you've answered my question but I'm confused about the term "geodesics experience a relative acceleration". Geodesics being the shortest paths through warped spacetime, how could those paths accelerate? How is it that a path can accelerate? $\endgroup$ – dcgeorge Jul 11 '18 at 15:35
  • $\begingroup$ Also, you say the marker particles move through spacetime but how is that possible? Since they are hypothetical particles which have no mass or charge, what moves them? It seems to me their apparent movement could only result from the expansion and/or contraction of the manifold. The coordinate system, itself, is what is undergoing the expansion and contraction. In which case, the markers wouldn't move relative to the coordinate system because they are just specific points in the system. $\endgroup$ – dcgeorge Jul 11 '18 at 16:21
  • $\begingroup$ 1. A particle, massive or massless, following a geodesic does not accelerate by definition. However here we are comparing two different geodesics. The curved spacetime makes them to have a relative acceleration, otherwise it would be a flat spacetime. 2. A free falling in a curved spacetime is described by the covariant derivative which contains terms related to the curvature; that is why a particle moves along a trajectory. $\endgroup$ – Michele Grosso Jul 12 '18 at 16:30

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