Sorry

I'm afraid I also don't know what this means. The metric assumes a mass distribution that we know isn't the mass distribution in nature. So in one reading of the prompt it's aphysical by simple observation. Does it perhaps reasonably approximate how spacetime behaves around a suitably isolated large mass? Maybe. But there're an awful lot of weasel words in that sentence - "reasonably", "approximate", "suitably". It's a bit like asking if Newtonian Mechanics or Nonrelativistic QM are physical. Strictly speaking, no. They're not accurate representations of the universe. They're limit cases of physical reality.

@Najawin The spirit of this is not to look for such difference. This is about fundamental issues with the metric itself that would play out even in idealized cases.

@JoeCharlier which fundamental issues?

@JoeCharlier But you asked if it's physical. It's aphysical, it doesn't correspond to physical reality. If you're asking about whether there are mathematical properties that the metric has that we would call aphysical so that it doesn't even work as a limiting case and suggests that GR might in some way be broken, or something, that's a much more complicated question and needs very robust fleshing out.

@Najawin I’m really asking about a specific experiment previously mentioned in these comments asking if the dilation experienced by a clock blasting off to infinity will match the dilation of a clock falling from infinity.

This wouldn’t necessarily require an issue with GM just an issue with the boundary conditions used in the Schwarzschild metric.

A fuller explanation of where I’m going with this can be found here: https://apps.apple.com/us/app/aexels/id935727868

@ArmandodiMatteo I’m interested in comparing the dilation of clocks blasting off with the dilation of clocks falling towards a mass.

@JoeCharlier Is this equivalent to the Schwarzchild metric, assuming GR? That is, iff this is the case - time dilation in each direction is equivalent, the mass distribution of the universe is what the Schwarzchild metric would predict? This seems implausible to me, but I could easily be mistaken. GR isn't my strong suit. If not, you're just asking a different question entirely, no?

@Najawin I not entirely following your comment. Just to reiterate, SM says the two clocks will be experiencing the exact same dilation. I have reason to believe that if such an experiment were performed the two clocks would experience different dilations.

@JoeCharlier aren't those just the time reversal of each other? What am I missing?

@JoeCharlier Okay, sure, whatever. Putting aside whether or not this is true, is this equivalent to the Schwarzchild Metric? Is the only metric where this holds the Schwarzchild metric and in all other cases it fails to obtain?

If the answer is no, you're just not asking about the Schwarzchild metric. You're asking about a specific physics experiment. You don't care about any aspect of the issue except for this one bit, so ask about this one bit.

Does it have to be accurate arbitrarily close to the central singularity? Only at distances much larger than one Planck length from the central singularity? Only outside the event horizon? Only at distances much larger than one Planck length from the event horizon?

@ArmandodiMatteo Ultimately this question is looking at issues beyond those related to the singularity or black holes. Plus I doubt any relevant data related to black holes will be collected in our life times. So, I have no problem with excluding a Planck length outside the event horizon inward from this question.

I might note however that if it does have problems on those ranges it might not bode well for the metric as a whole.

@JoeCharlier "Plus I doubt any relevant data related to black holes will be collected in our life times."

It's already being collected (very-long-baseline interferometry, gravitational waves from black hole mergers)...

@ArmandodiMatteo Data related to dilation?

@JoeCharlier I'm not sure of the details off the top of my head, but I think so https://en.wikipedia.org/wiki/Tests_of_general_relativity#Strong_field_tests

Not sure what this means. Around a spherical body like the Earth it’s pretty well tested experimentally (in the low field limit). But there are lots of bodies everywhere and no spherical symmetry so the metric just does not apply.

@mariopasquato Certainly, this only applies to (non-rotating) spherical bodies. The metric has been tested by comparing frames at constant gravity potentials. But, it also says that an object falling at escape velocity will experience the same dilation as an object blasting off at escape velocity. To my knowledge this has never been tested experimentally. (It also has issues with Black Holes but I assume that will not be experimentally tested anytime soon)

@JoeCharlier So you question is whether experiments will disprove predictions based on the Schwarzschild metric in its domain of applicability as understood within General Relativity? Can you describe in detail the experiment you have in mind?

@mariopasquato Yes exactly. It’s a little awkward to explain it fully within this app, but, briefly, consider 4 clocks: W, X, Y and Z. W at infinity, X falling from infinity, Y sitting on a platform r above the surface of a non rotating sphere and Z blasting off the sphere to infinity. X, Y and Z all meet at r at the same moment. The Schwarzschild metric says the Lorentz factor of the clocks is W < Y < X = Z.

However, perhaps an experiment would show W = X < Y < Z. Or to be exact that: gamma(v,v_e)=gamma(|v-v_e|) where v and v_e are vector quantities v representing the velocity of the clock and v_e representing the escape velocity of the sphere at each point pointing towards the center.

@JoeCharlier not anywhere near escape velocity, but time being constant along the geoid (i.e., the kinematic time dilation at the equator due to revolving around the centre of the Earth being equal to the gravitational time dilation at the poles due to being closer to the centre of the Earth) is pretty well established (if not, atomic clocks would have to be adjusted not only for elevation but also for latitude)

@ArmandodiMatteo This is a good point. Latitude comparison experiments have been performed?

@JoeCharlier https://en.wikipedia.org/wiki/Tests_of_general_relativity#Gravitational_redshift_and_time_dilation