Question: Do black holes exist or not? I know there's been a lot of controversy around this point. What are the arguments from both sides?

Susan Cartwright answered on 16 Jun 2015:

This is an excellent question. Most physicists would agree that there isn’t really a controversy, but it is definitely true that direct evidence is lacking.
Black holes are predicted to exist by general relativity. The argument is essentially that if a massive object is sufficiently dense, its escape velocity will eventually exceed the speed of light. Although the calculation is done in general relativity, in fact Newton’s law of gravity gives the right answer: the escape velocity from a spherical object of mass M and radius R is given by the square root of 2GM/R. If we set this equal to c and solve for R, we get R = 2GM/c^2. This is called the Schwarzschild radius, and works out at about 3 km per solar mass (so a black hole 10x the mass of the Sun has a radius of 30 km). If general relativity is right, then anything that collapses under gravity to less than its Schwarzschild radius will become a black hole (there are slight complications if the object is spinning, but that’s basically it).

When massive stars explode as supernovae, their central cores collapse into dense objects. In most cases, the dense object is a thing we call a neutron star – a packed-together ball of neutrons, basically a single atomic nucleus 20 km across and weighing about 1.5 times as much as the Sun. We KNOW neutron stars exist: we see them as pulsars, and can establish the masses and radii of those pulsars helpful enough to be in a binary orbit with another star.

According to a combination of general relativity and nuclear physics, neutron stars are not stable above a mass about three times that of the Sun – anything heavier must collapse into a black hole. We definitely do see compact objects with masses greater than three solar masses, so according to theory these should be black holes. The question is, what observational evidence can we muster to show that this is really what they are?

The point about black holes is that they have an event horizon – that is, the object itself is smaller than the Schwarzschild radius (in general relativity, the object collapses all the way down to zero size, but that is not to be believed because quantum effects come into play at small sizes, and we do not have a quantum theory of gravity yet). Nothing can emerge from below the Schwarzschild radius, so it acts as a horizon – you can’t see past it, hence the term “event horizon”. Can we demonstrate that the things that we think are black holes have event horizons and not solid surfaces?

The answer is that we do have some evidence in favour of this. Many compact objects are in binary orbit with another star, and if the binary is close enough the compact object will draw material off the other star and attract it towards itself. If the object has a surface, the added material falls on to the surface and heats up, eventually reaching the point at which nuclear reactions set in. At this point there is a small nuclear explosion which blows off the added material and the cycle starts again. It turns out that we see this behaviour for the compact objects with masses about 1.5 times the Sun’s, but we do NOT see it for objects with masses >3 times the Sun’s – which is just what we would expect if they have event horizons instead of solid surfaces (once the material has gone inside the event horizon, it is not coming back out).

Other points in favour of the existence of black holes are that we don’t see any emission from these should-be-black-holes that cannot be explained as resulting from the material being drawn in, whereas with neutron stars we definitely have emission that is coming from the neutron star itself, and that there is no evidence for a massive object with a radius which is smaller than its event horizon ought to be.

As far as I know, there is no evidence that these things are not black holes – it’s just that the evidence I summarised above is all rather indirect, and we don’t have smoking-gun proof.