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What would happen if a planet's escape velocity exceeded the speed of light? Would it also collapse into a black hole (by Heisenberg's uncertainty principle and Pauli's exclusion principle) or would it just remain as it is?

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    $\begingroup$ If its escape velocity exceeded the speed of light, it would already be a black hole. $\endgroup$ – D. Halsey Feb 19 '19 at 1:59
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At that point, it becomes a black hole. No other stable options exist. This fact is a direct consequence of general relativity.

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  • $\begingroup$ Could you explain the process? $\endgroup$ – Shreyas JV Feb 19 '19 at 1:37
  • $\begingroup$ This process is very well-described in a variety of sources; try a search for "black hole" in wikipedia and if there is anything you find unclear there, come back here and we can go through it with you. $\endgroup$ – niels nielsen Feb 19 '19 at 1:50
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IT depends, ultimately, on how you want to look at it. If you a mechanism, then you'll have to read deeper yourself and then come back with better posed questions.

Anyway, before general relativity, the answer to your question was by John Mitchell who conceptualized the so called "dark star" in Newtonian physics, and it is defined exactly as you wish ($v_{esc} \geq c$).

In general relativity, this concept is more rigorously defined (and explored) and is called a "black hole." For instance, the introduction of P.K. Townsend's book might be helpful which discusses gravitational collapse. General relativity has been extremely well verified, and the observation of gravitational waves from black hole binaries is the latest verification.

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