# Do black holes have a limit of mass?

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?)?
• 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. Feb 5, 2019 at 21:08
• Our Universe has a large mass, before the Big Bang it looks like a black hole. Feb 5, 2019 at 21:21
• @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
– user4552
Feb 5, 2019 at 21:29
• @BenCrowell It seems that the mainstream believes in one legend, and I in another. Feb 5, 2019 at 21:46

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.

• 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.
– Void
Feb 5, 2019 at 21:16
• 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
– user87745
Feb 5, 2019 at 21:17
• 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) Feb 5, 2019 at 21:34
• @Void How does making the black hole horizon larger than observable universe create a naked singularity? Could you explain how that works? Thank you in advance. Jul 27, 2022 at 21:24

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  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(!)  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.

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

 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.