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How can I make a black hole by changing a metric background? I have one metric background that isn't black hole. I want to convert a metric to black hole by changing the coordinates. What should I do?

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closed as unclear what you're asking by peterh, DilithiumMatrix, AccidentalFourierTransform, Kyle Kanos, user36790 Nov 22 '16 at 15:03

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Hi @Marja.Kms, welcome to Physics.SE. Your question is currently quite unclear. Can you try to explain more thoroughly what you're trying to ask? For example, by "make a black hole" do you mean the formation of a black hole, or do you mean a mathematical description? $\endgroup$ – DilithiumMatrix Nov 22 '16 at 14:02
  • $\begingroup$ Hi @DilithiumMatrix, Thanks for your attention. I edited my question. $\endgroup$ – Marja.Kms Nov 22 '16 at 17:55
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    $\begingroup$ Comment to the post (v4): GR is a geometric theory independent of coordinates. Why should physics (i.e. whether there is a black hole or not) change because you change coordinates? $\endgroup$ – Qmechanic Nov 22 '16 at 18:14
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$$g_{\mu \nu} dx^{\mu} dx^{\nu} = \left(1 - \frac{r_s}{r}\right) c^2 dt^2 - \left(1 - \frac{r_s}{r}\right)^{-1} dr^2 - r^2 \left( d\theta^2 + \sin^2 \theta d\varphi^2 \right). $$

This is a "metric background" as you would call it corresponding to the Schwarzschild geometry. It describes a stationary non-rotating black hole with no electromagnetic charge.

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