# Is there a limit to the size of a black hole?

The mass of a star is limited to about a couple of hundred solar masses. The fusion rate scales strongly with density (which is why the most massive stars have extremely short lifetimes) so if a star was massive enough (above the Eddington limit) then the radiation pressure would blow it apart.

Now a black hole also has radiation, but by definition it is not capable of escaping due to gravity. But is there in some way a limit of the size. Imagine that all the matter in the universe formed a black hole. Should that be possible or is there a law which forbids creating it?

• "Imagine that all the matter in the universe formed a black hole..." Isn't that a description of the universe pre-big bang? (At least by popular models) Mar 9 '16 at 23:25

General Relativity does not limit the size of a black hole, and we have good (indirect) observations of black holes with a mass of more than a billion suns.

Black holes are not object that are held together by gravity, and which could be ripped apart if forces opposing that gravity were increased. They are (in GR) singularities: a complete collapse of the matter to a point. There is no "object" inside a black hole that could be emitting radiation.

Now if all the matter in the universe were to be a black hole, then that singularity would be in all our futures. We wouldn't "see" the singularity because it is in the future, never in the past. In fact a universe in which is one black hole could look rather like the one in which we are living.

• Why can't there be any radiation within a BH? Isn't there enough space just within the Schwarzschild radius? Mar 9 '16 at 20:40
• There can be radiation inside the black hole, but it isn't going anywhere but to the singularity. Once something crosses the event horizon, the singularity is in its future, and it is certain to reach it in a finite amount of time. There can't be any radiation coming from the singularity, because the singularity is never in the past. (Time is weird inside a black hole, but look up "penrose diagram" ) Mar 9 '16 at 21:54

There's no theoretical limit. If you had enough energy to move stars or galaxies, you could in theory keep feeding a black hole until it became enormously large, larger even than the Milky way for example. But there are practical limits past which black holes are unlikely to grow.

The two reasons for this are that 1), black holes aren't efficient at taking in matter. They can spit out as much as 90% of the energy from the matter that falls into them, and 2) once they reach a certain size, black holes are too large to form accretion disks, so matter tends to orbit around them rather than funnel into them.

Source and Source.

As to your 2nd question

Imagine that all the matter in the universe formed a black hole. Should that be possible or is there a law which forbids creating it?

I've pondered this one myself and I have no idea the answer. Is there a size past which Dark Energy would overcome gravitation? Dark energy operating inside the black hole might overcome the gravitation past a certain size, but that's just my novice speculation and I think the black hole would need to be billions of light years across for that to happen.

I don't know the answer to that one. I'd be curious if anyone does though.

According to an article in the NewScientist, there is a natural size limit:

When black holes at the hearts of galaxies swell to 50 billion times the mass of our sun, they may lose the discs of gas they use as cosmic feedlots.

Most galaxies host a supermassive black hole at their centre. Around this is a region of space where gas settles into an orbiting disc. The gas can lose energy and fall inwards, feeding the black hole. But these discs are known to be unstable and prone to crumbling into stars.

But there were observational hints that such a limit should exist. In 2008, an independent group led by Priya Natarajan of Yale University and Ezequiel Treister of the University of Concepcion in Chile considered how much black holes feasted in the early universe and the free gas available for them to swallow in recent times.

Given how much black holes have eaten since the dawn of the universe, they argued, the greediest ones could have grown to a size of about 50 billion solar masses.

So this really amounts to a semantic argument. The upper limit would not be a pyhsical limit—if you could somehow bring two of these 50-billion-mass behemoths together they would merge to form one of 100 billion solar masses—but one of what I'll call "eating opportunity." Eventually a black hole will eat all the gas within an accessible distance and won't be able to grow anymore.