If we create a black hole by compressing a mass $M$ to a radius smaller than Schwarzschild Radius, would the gravitational force of the mass $M$ (now a black hole) be different before and after becoming a black hole?

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    $\begingroup$ No, as long as the BH doesn't gain angular momentum or cahrge during collapsing. $\endgroup$
    – KP99
    Sep 25 at 15:36
  • $\begingroup$ Are you counting the energy & pressure required to compress the matter? $\endgroup$
    – PM 2Ring
    Sep 25 at 15:57
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/664342/2451 and links therein. $\endgroup$
    – Qmechanic
    Sep 25 at 16:05
  • $\begingroup$ @safesphere So does that mean black holes are impossible objects in GR? $\endgroup$
    – KP99
    Sep 26 at 16:04

The Gravitational force at any given point that existed outside the body before compression would be the same as before. The difference is when you moved a lot closer to it, in regions that used to be inside the star (say), gravity starts getting much stronger and stranger.

This is all from the Schwartzchild Solution to Einstein's equations. Schwartzchild simply solved the equations of General Relativity (i.e. showing the geometry of space time) for a point mass of zero size. It matches up with Newton's laws until you get very close. The attached equation shows the Schwartzchild potential (i.e. energy for a given mass orbiting). The first term is regular Newtonian Gravity, the second is centrifugal force, and the third is the one newly discovered with relativity. Because of the c^2 in the denominator, it is vanishingly small until the radius gets really small and/or the mass gets really big. This term is responsible for the precession of Mercury, and all the strangeness around black holes


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    $\begingroup$ BTW, GR effects are only responsible for less than 10% of the precession of Mercury's orbit. See en.wikipedia.org/wiki/… $\endgroup$
    – PM 2Ring
    Sep 25 at 19:25
  • $\begingroup$ Really, I did not realize that! Thanks $\endgroup$
    – RC_23
    Sep 25 at 21:38

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