In GR, space and time form a single geometry called space-time, and gravity is a curvature of this geometry. Within this geometry, there are 3 spacial dimension

In GR, space and time form a single geometry called space-time, and gravity is a curvature of this geometry. Within this geometry, there are 3 spacial dimensions, and 1 time dimension. However, there is no universal axis. In the same way that different observers may disagree on which direction x is, they could also disagree on which direction t is. In the context of a black hole, we can compare the coordinate system that someone far away would use, with the coordinate system of someone near the black hole. For someone far away, the center of the black hole is just that. A point in 3 dimensional space causing a gravitatational field. However as you aproach the black hole, your natural coordinate system starts to warp relative to a distant observer. Your time axis begins to point more towards the center of the black hole. At the point you cross the event horizon, your perspective of "future" points entirely in what a distant observer would call a spatial direction: towards the center of the black hole. In particular, the black hole singularity is no longer a point in space, but a point in time. Every observer within the event horizon sees a universe where the future is an infinitly dense singularity that all geodesics will arrive at. Compare this with our current universe. We see a universe where the past is an infinitely dense singularity that all geodesics originate from.