Classically, the Schwarzschild singularity is a 3-dimensional spatial boundary of 4-dimensional spacetime: the time dimension expires at the singular surface.

Quantum mechanically, if unitarity holds, then the singularity is a 2-dimensional spatial surface (per Bekenstein-Hawking) evolving in an emergent time dimension.

Is the singular surface a 2-brane?

  Kerr black hole