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  1. If you have a bunch of gas and increase its mass, gravity combines it into a planet.
  2. If you have a planet and increase its mass, gravity forces the planet to undergo nuclear fusion, turning it into a star.
  3. If you have a star and increase its mass, the gravitational collapse surpasses any thermal or degeneration pressure and turns the star into a black hole.
  4. If you have a black hole and increase its mass, would gravity turn it into another thing? Do black holes have a limit of mass or they can go to infinity without undergoing any change (like nebula > planet > star > black hole > ...black hole?)?
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  • $\begingroup$ If we just think about mass density then the objects you described cover the full spectrum of possibilities from almost zero density to theoretical infinite density. $\endgroup$ – TheNaturalTanuki Feb 5 at 21:08
  • $\begingroup$ Our Universe has a large mass, before the Big Bang it looks like a black hole. $\endgroup$ – Alex Trounev Feb 5 at 21:21
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    $\begingroup$ @AlexTrounev: Our Universe has a large mass, before the Big Bang it looks like a black hole. Not true, see (1) physics.stackexchange.com/q/5150 , (2) physics.stackexchange.com/q/3294 $\endgroup$ – Ben Crowell Feb 5 at 21:29
  • $\begingroup$ @BenCrowell It seems that the mainstream believes in one legend, and I in another. $\endgroup$ – Alex Trounev Feb 5 at 21:46
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The rules of classical general relativity say that when you add mass to a black hole, you get a larger black hole. If you add angular momentum to a black hole at a greater rate than that at which you add mass, it would theoretically be possible to get a Kerr black hole with $a \gt M$, which would convert the black hole to a naked singularity, but the rules of black hole thermodyanamics say that a black hole with $a = M$ has zero temeperature, so creating a naked singularity in this way is believed to be impossible.

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    $\begingroup$ One more note, it is also possible to make the black hole so large its horizon is larger than the cosmological (dS) horizon. Then it also becomes a naked singularity. $\endgroup$ – Void Feb 5 at 21:16
  • $\begingroup$ Also, in a universe with a positive cosmological constant, if the mass of a black hole exceeds $\frac{1}{3\sqrt{\Lambda}}$ then the black hole would become naked. I suppose there should be some censorship argument so as to naturally prevent such a scenario in a generic situation. Edit: @Void, your comment appeared just when I pressed enter to post my comment :P Maybe you can also help me with a related old unanswered question of mine: physics.stackexchange.com/q/337760 $\endgroup$ – Dvij Mankad Feb 5 at 21:17
  • $\begingroup$ Thank you . Yes, that is the exception. (In these cases, the extremal black hole will be zero-temperature, too, so one would presume that this would prevent any further matter infall) $\endgroup$ – Jerry Schirmer Feb 5 at 21:34
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There is the tantalising possibility that adding more matter to a black hole can destroy it, by making its horizon disappear. Indeed a Kerr-Newman black hole, i.e. one that spins and that has an electric charge, must satisfy the relation $m^2 \ge a^2 + e^2$ where $m$ is the mass, $e$ the charge, and $a=J/m$ is the angular momentum per unit of mass (geometrised units G = c = 1 being used throughout). So as @Jerry-Shirmer stated, if the added matter contributes more spin or more charge than mass, then the black hole could be destroyed. There is a long history of research into proving that this cannot actually happen when properly modelling the motion of the matter falling into the black hole. The oldest result is, I think, that of Wald [1] about falling test particles (that is to say, loosely, bits of matter small enough that they do not affect the geometry of spacetime). The question of whether more realistic in-falling matter could destroy a blackhole has been discussed for many years. The latest publication I know of is another paper by Wald(!) [2] and the answer is no! You will find all the bibliography you want in that one. The only assumption is that the matter satisfies the so-called null energy condition, which is valid for all matter we have observed.

[1] Wald, Robert (Feb. 1974). “Gedanken experiments to destroy a black hole”. In: Annals of Physics 82.2, pp. 548–556.

[2] Wald, Robert M. (Aug. 2018). “Kerr–Newman black holes cannot be over-charged or over-spun”. In: Inter- national Journal of Modern Physics D 27.11, p. 1843003.

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