The anomaly of spiral galaxies and the need for dark matter 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.