How does spaghettification work in general relativity? Imagine a neutron star is being consumed by a black hole, so I think matter from the star is being stretched as it follows the curvature of the spacetime around the black hole. If that is the case what forces is stretching the degenerate matter?
 A: Spaghettification is not just a General Relativistic effect and not just confined to strong gravity regimes. It is a consequence of different parts of an extended body feeling different gravitational forces and this produces a differential force acting across that body - a.k.a. a tidal force.
In the specific case of an object of finite size falling towards a source of gravity, there are two such differential gravitational forces to consider, which are of roughly similar magnitude.
The first is that gravity is stronger the closer to the source of gravity. This produces a differential force characterised by the gradient of the gravitational field multiplied by the radial extent of the falling body, and acts as a stretching force in the radial direction.
The second, less recognised, effect is that the gravitational field points radially inward. For an object of finite width, this means there is a component of the gravitational field that is resolved towards the centre of the body and that gets larger as you move towards the left and right hand edges of the body. This creates a compressive force at right angles to the stretching force above, and also has a size roughly equal to the gradient of the gravitational field multiplied by the tangential extent of the body.
Taken together, the radial stretching force and the tangential compressive force have become popularly known as spaghettification.
A: Tidal forces: gravitational forces on the matter that is closer to the black hole, is way higher than gravitational forces on matter just a little distance away from the black hole. this happens on Earth too, but it is at strong gravitational fields that this effect becomes highly noticable
A: I completely agree with Rob Jeffries and just want add another aspect.
Imagine marbles are released one shortly after the other towards a mass, a planet, a star or a black hole, e.g. During their free fall the distance between these marbles will increase, because the closer to the mass the more gravitational attraction they feel.
So, the radial chain of these marbles gets stretched because each one is in free fall.
Tidal forces occur, if things are not in free fall. Imagine now that the marbles are connected with each other to form a chain. The chain is released and falls radially. Then there is one marble in between which is in free fall, but all others below and above it aren't, because they are forced to keep constant distances. This force which "try's" to stretch the chain is called tidal force.
One also talks about tidal gravity because tidal forces are due to curved spacetime.
A: I believe the question is asking to explain spaghettificiation without invoking the classical idea of gravity as a force. In the context of an astronaut falling into a black hole:
As you approach the event horizon your feet will experience a much smaller spatial dimension compared to your head. While neither your head nor feet have accelerated, your feet now have less distance to travel. The effect looks an awful lot like acceleration, which is why it's tempting to describe it as a force. But it might alternately be thought of as your feet's momentum carrying them away from your head faster than the cohesive forces in your body can cope with. Hence spaghettification.
