# Can there be a black hole as big as the space between any two neighbor stars?

Can there be a black hole as big as the space between any to neighbor stars?

e.g. lets say we Proxima Centauri/Alpha Centauri A and our Sun. The distance would be about 40,208,000,000,000 km.

So the questions is, if its possible for a black to be as bit as that under the laws of physics?

• Have you tried working out the required mass to create that Schwarzchild radius and then comparing it to the mass of galaxies and the universe ? – StephenG Feb 12 '18 at 19:01

The Schwarzschild radius is the maximum radius of a black hole with mass M. It is defined as:

$$r_s = \frac{2MG}{c^2}$$

where M is the mass of the hole, G is the gravitational constant, and c is the speed of light. Solving for $r_s=40,208,000,000,000 km$, you get $M\approx 2.71*10^{43} kg$. For reference, our galaxy is estimated to have a mass of $6*10^{42} kg$. A quick google search indicates that the heaviest black hole we know about is at only $4.18*10^{40}kg$.

I'll leave the actual conjecturing up to my betters, but I'd expect that a black hole that's orders of magnitude larger than anything we've ever observed is highly unlikely.

• so basically, you say that, for now at least, we consider this impossible? – aurelius Feb 13 '18 at 8:39

Most likely there are no black holes like that in the observable universe, but it is possible that in a very distant future black holes like that could form as a result of many mergers of black holes from centers of galaxies.

As Jakob Lovern already answered, the mass for such a black hole would have to be on the order of $10^{13} \,M_\odot$. This is several times larger than the mass of the Milky Way, but in terms of the largest scale of gravitationally bound systems (like superclusters) it is not that big. So the question is: how can such a mass end up inside a black hole.

To answer that we have to consider the long term evolution of the gravitationally bound systems such as galaxies, galactic groups and larger. The timescales involved greatly exceed the current age of the Universe or the lifetime of stars. At this timescale the galaxy consist of a large number of star remnants orbiting the galactic center with its central black hole. Due to the occasional gravitational slingshot some stars would gain enough velocity and leave the galaxy carrying away angular momentum and kinetic energy. This is similar to evaporation of a water droplet with fastest molecules escaping and cooling the remainder. The remaining stars would thus become closer to each other and to the center and faster moving. At the same time orbits of stars closest to the central black hole would decay because of emitted gravitational radiation and they would eventually accrete inside. As a result of this two processes central black hole would accumulate about 1-10% of all star mass, while the rest of stars would 'evaporate' leaving the galaxy. As a result the central black holes in the galaxy would have mass about $10^9 - 10^{10}\,M_\odot$. This happens on timescale of about $10^{30}\,\text{yr}$.

Now consider a galactic supercluster (Not all superclusters are gravitationally bound, but some are and those would likely remain bound on the timescales we are considering). After the 'evaporation' of most of the stars we would have a large number of big black holes orbiting each other surrounded by a 'gas' of stellar remnants providing 'friction'. So one could expect that a similar process of 'evaporation' would proceed on this greater timescale: some giant black holes would escape the cluster while some would coalesce forming one super black hole at the center of such supercluster. The timescale for that would be about $10^{33}\,\text{yr}$. And so this huge black hole has the potential to have mass $10^{12}-10^{13}\,M_\odot$.

There are many unknowns in the scenario outlined above:

• What is the nature of dark energy, and does its value changes over time? The answer would affect the longterm fate of the largest scale structures.
• What is the nature of dark matter and how dark matter halo of galaxies would behave over the time intervals we considered here?
• What precise fraction of stars of the galaxy would end up in black hole, what fraction of black holes coalesce into the super black hole?

For more details see the chapter 3 of the survey:

Adams, Fred C., and Gregory Laughlin. A dying universe: the long-term fate and evolution of astrophysical objects. Reviews of Modern Physics 69.2 (1997): 337, doi , arXiv.