Can Black Hole Evaporation Preserve Entropy While Losing Mass?

[The Lobster]

During black hole thermal radiation can mass be radiated while entropy stays? Is it possible that entropy stays in the singularity?

 

[zhermes]

According to general relativity (and a few contributions from high-energy physics) Black holes should obey the 'no-hair theorem', which states that there are only a few very basic parameters which fully describe the nature of a black-hole (note: 'black-hole' does not equal 'singularity'). Entropy is not one of the fundamental parameters---instead, entropy is a function of the black hole's surface area, which is a function of its mass (and a few other things). If the mass decreases, so does the entropy. If there is no mass, there is no entropy.