Please could some explain this to me - I understand that some galaxies are rotating with a speed that the stars on the outer reaches should not be held within the spiral given the observed matter and consequent gravitational field it forms. As a consequence of this, we are looking for dark matter that would compensate for this imbalance. But my question is this, how do we know that a black hole found at the centre of many galaxies is not providing the ‘extra’ gravitional curved space time required to hold the spiral galaxy together ?
Supermassive black holes are really small, compared to the mass of the galaxy.
We know how big the black hole is, because we can see the stars in the centre of galaxies orbiting it. So in a typical spiral galaxy the black hole has a mass of a few million suns. But the galaxy has a mass of a few trillion suns.
The black hole dominates the gravity in the cluster at the very centre of a galaxy, but out by us, it is entirely negligible
You don't need to use general relativity for this. Relativity is significant when you are close to a black hole, but if you are far from it, then ordinary Newtonian gravity is an excellent approximation. The force of gravity drops in inverse proportion to the square of the distance, which means that something as small as a supermassive black hole is much too tiny to have any effect on the the orbital speeds of most of the galaxy.
To model the orbital speeds there has to be something with a mass of trillions of suns, which entirely surrounds the disk of the galaxy, which the stars can pass through without friction and is completely invisible. Finding that is the challenge of dark matter.
Don't think of black holes as fantastic objects that exert some kind of super-strong gravity. They do indeed do that, but only in zones close to the event horizon (i.e. only in their very immediate neighborhoods). If the Sun were replaced by a black hole of the same mass, the Earth would still continue to orbit as normal.
In the same way, the supermassive black holes at the center of galaxies simply acts as a supermassive body of a few million solar masses. The gravitational effects of that supermassive black hole on the rest of the galaxy are well approximated by Newton's laws. For the purpose of the dark matter problem, it doesn't matter if the body at the center of galaxies is a black hole, a star, etc - they all have the same effect on the outskirts of the galaxy.
Besides the fact that the central black holes really aren't all that massive compared to the galaxy, there is another more fundamental reason they can't explain the overly rapid revolution of the outer stars. The problem is that the outer stars are moving faster than they should be compared to the inner stars. If you make the central black hole a trillion times more massive, the outer stars would have to be moving faster, but the inner stars would have to be moving a lot faster.
But if you spread out a bunch of mass throughout the galaxy, then the inner stars don't have to be going so much faster to stay in orbit, because there's only so much extra mass inside their orbit. But the outer stars are influenced by more mass and so are moving faster than you expect.
Smaller, widely-scattered primordial black holes are a dark-horse candidate for being the dark matter, or maybe a part of it, but that's considered unlikely at this point.