This is a space-time diagram of a neutron star. The depth of the distortion suggests that you would need a very large speed to leave the surface of a neutron star. The escape velocity from a typical neutron star is 120,000 miles/s. Could there be anything more extreme than a neutron star? The answer is a surprising, shocking yes. Remember that in the death throes of a massive star, the only thing that stopped gravity from crushing the neutron star even further was the strong force. A star much greater than 8 times the mass of our sun is capable of squeezing the core so hard, that not even the strong force can resist. The strong force is a star's last call to arms. If the strong force is defeated, there is nothing in the universe that can stop gravity, and so the star's core is literally crushed out of existence. This is called a black hole.
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