Are there 3D singularities in general relativity?

Question

In the commonly considered spacetimes with singularities, the singularities - to my knowledge - always have less than 3 spatial dimensions:

• The singularity of the Schwarzschild spacetime (describing stationary black holes), the Vayidia spacetime (describing radiating spacetime), or the FLRW spacetime (describing the Universe) manifests as a single 0D point in 3D space (line in 4D spacetime).
• The Kerr, the Reissner-Nords or the Kerr-Newmann spacetime (describing charged and/or rotating black holes) have singularities manifesting as a closed 2D surface. While the space inside of these is unreachable, it's no singularity, as there's no infinite/undetermined scalar quantity, and can be described within the realms of GR. (Whether these descriptions are physical are another question.)

Is there any known a) physical and b) unphysical (containing exotic matter or negative energy) solution of the Einstein equation that gives a spacetime with a 3D physical singularity?

If not, is there a theorem/property that mathematically rules out the existence of such a spacetime?

Answer 1

Your premise mistaken. The dimensionality of singularities in GR is undefined. The metric breaks down at a singularity, so we can't define how many dimensions it has. You can try to define the dimensionality based on what it looks like on a Penrose diagram, but that's ambiguous because you have a lot of freedom in how to draw the Penrose diagram. On a standard Penrose diagram for a black hole, the singularity looks like a 3-surface, but that doesn't really mean that it's 3-dimensional.