Sorta. Hawking radiation should cause black holes to radiate away all their mass eventually, but since it’s inversely proportional to the mass, small enough black holes should radiate very quickly. Hawking speculated (giving a few arguments) that black holes couldn’t form with masses below about the Planck mass, but it’s not settled. Note that the Planck scale (e.g. the Planck energy is the one where we expect quantum gravity to become important—so for example we can’t be confident that Hawking radiation still occurs, and some believe it doesn’t.
The reduced Compton wavelength of a particle is defined as the reduced wavelength (angular wavelength aka wavelength / 2pi) of a photon with the same energy (hbar c/lambdabar) as the mass energy of the particle (mc^2). That is, ƛ. The reduced Compton wavelength appears in quantum wave equations for particles, thus giving a scale.
The Planck mass and length are defined so that the gravitational energy of two Planck masses that are a Planck length apart is equal to the mass energy and also equal to the energy of a photon with reduced wavelength the Planck length. That is, . This gives us
Sorta. Hawking radiation should cause black holes to radiate away all their mass eventually, but since it’s inversely proportional to the mass, small enough black holes should radiate very quickly. Hawking speculated (giving a few arguments) that black holes couldn’t form with masses below about the Planck mass, but it’s not settled. Note that the Planck scale (e.g. the Planck energy is the one where we expect quantum gravity to become important—so for example we can’t be confident that Hawking radiation still occurs, and some believe it doesn’t.
Some conjecture that black holes should radiate away entirely (which would allow black holes to exist below the Planck mass even if for some reason you couldn’t make them without making a bigger one first). Others think that they should radiate away the mass but leave a ‘naked’ singularity without an event horizon (though many believe this is impossible). Some alternatively think that they’ll be stable around the Planck mass due to a quantized gap preventing them from releasing Hawking radiation or absorbing energy, which make them act like a weakly interacting massive particle (WIMP) and thus be a dark matter candidate, an idea similar to primordial black hole theories.
The way I think about the Planck units is:
The reduced Compton wavelength of a particle is defined as the reduced wavelength (angular wavelength aka wavelength / 2pi) of a photon with the same energy (hbar c/lambdabar) as the mass energy of the particle (mc^2). That is,ƛ
The Planck mass and length are defined so that the gravitational energy of two Planck masses that are a Planck length apart is equal to the mass energy and also equal to the energy of a photon with reduced wavelength the Planck length. That is,