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Assume one initially has perfectly flat Minkowski vacuum. At some point in this Gedankenexperiment a point mass spontaneously appears at some location in Minkowski creating a Schwarzschild geometry. At some interval from the location of this point mass, how much proper time does it take for the space to appear Minkowski? Is there some sort of gradual change in the metric from Minkowski to Schwarzschild or does this change occur instantaneously?

Qmechanic
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twidle
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    Well, you can't make mass appear out of nowhere, that violates Einstein's equations. But any change will propagate at the speed of light, never instantaneously. – Javier Nov 21 '17 at 15:44
  • What would happen if the Sun vanished instantaneously? –  Nov 21 '17 at 15:55
  • Can't make a mass appear out of nowhere, but you can shake a mass or, you can have two masses that orbit a common barycenter, and when you do that, you get gravitational radiation. – Solomon Slow Nov 21 '17 at 15:55
  • @Countto10 As Javier mentioned, the very idea of an instant change is non-physical. Even in a simple case of a "rubber sheet", how can you possibly make a "dent" in it instantly without ripping a hole in it? So the speed of change is an integral part of the problem formulation. Then the result reported earlier on this forum is rather interesting. If you tow away the Sun at any speed under the speed of light, then the Earth at any time would be attracted to the actual instant position of the Sun with no 8-minute delay. So in these terms the change is instantaneous. Same with electric charges. – safesphere Nov 21 '17 at 16:23
  • "a point mass spontaneously appears at some location in Minkowski creating a Schwarzschild geometry" - a propagating disturbance of the spacetime geometry is a gravitational wave. In the context of GR, there is no monopole (or dipole for that matter) gravitational radiation but a point mass spontaneously appearing would create monopole gravitational radiation (just as the sudden appearance of an isolated point charge would create monopole electromagnetic radiation) and so is inconsistent with GR. – Alfred Centauri Nov 21 '17 at 18:24
  • @safesphere thank you. As usual I kinda jump to pop sci answers I feel are reliable, and also, in this case, I wondered if the Generally, no of Jamal's answer was a caveat for something I missed, but I will read over that again. I do take your point, if I have it right, that you can't arbitrarily apply the established rules of physics to non physical / impossible situations. I will bear that in mind, thank you for taking the time to point this out. –  Nov 21 '17 at 22:45

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Generally, no. Suppose we have empty space $T_{\mu\nu} = 0$, in which case the field equations are,

$$R_{\mu\nu}-\frac12 g_{\mu\nu}R = 0$$

with solution $g_{\mu\nu} = \eta_{\mu\nu}$. Adding any kind of matter, we have a perturbation $\delta T_{\mu\nu}$, and we have that to first order $R_{\mu\nu} \sim \Delta_L h_{\mu\nu}$ where $h_{\mu\nu}$ is a perturbation.

How the curvature changes over time is then dictated by $h_{\mu\nu}$ and will depend on the problem. Since you inserted some new matter at some time, $\delta T_{\mu\nu}$ will be time dependent, and so we expect $h_{\mu\mu}$ to also be time dependent, not instantaneously changing the manifold.

JamalS
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