This is very likely to be the case, though no one has figured out a way to prove it since we dont have any black holes to study at close range!

The Planck conditions are believed to be represented by a set of elementary numbers that you can create, with a little dimensional analysis, from the fundimental constants G (Newtons Gravitation Constant), c (the speed of light) and h (Plancks Constant). What you get by combining these with the right powers are the Planck Length ( about 10^-33 centimeters), Planck mass (about 10^-5 grams) the Planck time (about 10^-43 seconds) and a Planck energy (about 10^19 GeV).

So far as we know, Einstein's general theory of relativity needs to be extended to include quantum mechanical effects. Theoreticians believe that these effects become important when you try to describ what happens near the so-called Singularity at the center of a black hole.

It is predicted that instead of the collapsing star contracting to infinite density, its final density at the Singularity will be limited by quantum gravity (and the presumed graininess of space and time) to about 10^94 grams per cubic centimeters, which is defined by taking the Planck mass of 10^-5 grams and dividing by the cube of the Planck length 10^-33 centimeters to get 10^-5 /10^-99 = 10^94 grams per cubic centimeters.

Physicists often find limits 'built into' various other physical phenomena, and the Planck limits seem a reasonable idea, though the scales are going to be incredibly, perhaps impossibly, hard to explore experimentally.

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