Singularities are still theoretical. We are fairly certain that black holes exist, but whether they are singularities is definitely undetermined.

I guess that any "normal" matter construct can have an anti-matter twin, so I'm not sure exactly what would prevent an anti-singularity from forming if singularities exist.

However, if an anti-singularity sucked in normal matter, it would necessarily lose mass and possibly lose its "anti-singularity" status once its density dropped below a certain level.

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"Barbarism is the natural state of mankind. Civilization is unnatural. It is a whim of circumstance. And barbarism must always ultimately triumph" -- Conan