Gravity Without Things: II. Falling Into a Black Hole Without Falling Through Space

If gravity is a changing pattern of spatial relations, what happens when we approach a black hole?

Far from the black hole, the difference is barely noticeable. As we approach it, the relations become increasingly differentiated. The geometry becomes progressively less like the approximately flat geometry of empty space.

But nothing special happens at the event horizon itself.

The horizon is not a surface on which space suddenly contracts, nor is it a boundary surrounding a region of unusually dense matter. An observer falling freely into a sufficiently large black hole would cross it without encountering a local physical barrier.

So what, then, is the horizon?

It is a boundary in the structure of possible relations.

Outside the horizon, there are possible future-directed paths that lead away from the black hole. At the horizon, the geometry changes so that the boundary between escape and non-escape is reached. Inside it, every future-directed causal path leads toward decreasing areal radius.

This is why the usual image of an object falling through space toward the centre can be misleading.

The object is not being dragged through some pre-existing spatial substance. Rather, the relational geometry determines what future-directed motion can mean.

Outside the horizon, moving inward is one possibility among others.

Inside it, moving toward smaller radius is no longer merely a direction one may choose. It is part of the structure of one's future.

The horizon therefore does not mark the place where gravity suddenly becomes stronger. It marks a transformation in the possibilities afforded by the geometry.

This gives the black hole a remarkable relational character.

The further inward we go, the more strongly the relations constrain what can happen next. The geometry does not simply tell us where an object is. It increasingly determines where it can become.

And this raises a final question.

If the relational structure can become so strongly constraining that escape ceases to be possible, what happens when we follow that structure all the way to the centre?

Perhaps we should not expect to find an extraordinarily small thing waiting there.

Perhaps we should expect the relations themselves to reach their limit.

That is where the singularity enters the story.