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Is the gravity of a black hole the same or more than the original star that created it, before the black hole gets more matter? Is the gravity proportional to the initial mass?

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    $\begingroup$ It will be close, but smaller. Gravitational waves generated during collapse will carry some mass/energy away. $\endgroup$
    – Alexander
    Mar 7 at 18:23

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The gravitational effect of a body depends mostly on two things. The mass of the body and the distance from the centre of mass of the body.

So if we keep those two things equal, then the gravitational effect will be the same (subject to the considerations below).

So if you are 10 AU from (the centre of) a star, and that star collapses to a black hole (without changing mass) then the gravitational effect of the mass at your position will be the same.

Of course the "surface gravity" will be very different. A consequence of a black hole is that the matter is all in a very small region of space. If you change your position in space (relative to the centre of mass) then the gravitational effects will be different.

There are a couple of provisos. Firstly, if the matter is not in the form of a spherical ball then the gravitational field around the body won’t be even. But if that asymmetric ball collapses into a symmetric black hole, the gravity will become symmetric. In the extreme case of a hollow sphere, there is no net gravitational field inside the sphere. But if that sphere is collapsed to a black hole, there will be a net gravitational field at points that were inside the shell.

Secondly, there are effects caused by the rotation and electric charge of the body. The electric charge won't change much as the body collapse, but the rotation will change.

Finally, in the practical collapse of matter to a black hole, mass will almost inevitably be lost. The process is energetic and radiation or neutrinos will be emitted. So the mass of the black hole won’t equal the mass of the progenitor star.

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    $\begingroup$ Lovely answer !!! This is specifically what I was looking for and would have asked a followup if you hadnt put this in -“ So if you are 10AU from (the centre of) a star, and that star collapses to to a black hole (without changing mass) then the gravitational effect of the mass at your position will be the same.” Unfortunately I can nor upvote as I am noob. Thanks @jamesk $\endgroup$
    – Solo Man
    Mar 7 at 6:28
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    $\begingroup$ Yes, in particular, should the Sun turn into a black hole (it can't on its own) the Earth and other objects in the Solar System would happily continue oribiting just as they are now (disregarding stuff such as the loss of mass/energy as mentioned above, or the possible/likely slight shift of the center of mass of the Solar System) $\endgroup$
    – scibuff
    Mar 7 at 20:48
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    $\begingroup$ @SoloMan Yes, it's a fact that sci-fi depictions of black holes has made surprising. Black holes do not actually have "stronger gravity" than other objects of comparable mass. If we model the Sun (or even the Earth) as a point-mass, you can find a radius where gravity would be "too strong for light to escape", just like with a black hole! The only difference is that radius is deep inside the Sun/Earth (where the point-mass approximation has long since broken down as a useful model). Black holes aren't stronger, they're just smaller; you can get closer to them without being inside them. $\endgroup$
    – Ben
    Mar 8 at 0:08

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