Is there a black hole minimum mass?
Abstract
Applying the first and generalized second laws of thermodynamics for a realistic process of near critical black hole formation, we derive an entropy bound, which is identical to Bekenstein’s one for radiation. Relying upon this bound, we derive an absolute minimum mass ∼0.04g_{*}m_{Pl}, where g_{*} and m_{Pl} is the effective degrees of freedom for the initial temperature and the Planck mass, respectively. Since this minimum mass coincides with the lower bound on masses of which black holes can be regarded as classical against the Hawking evaporation, the thermodynamical argument will not prohibit the formation of the smallest classical black hole. For more general situations, we derive a minimum mass, which may depend on the initial value for entropy per particle. For primordial black holes, however, we show that this minimum mass can not be much greater than the Planck mass at any formation epoch of the Universe, as long as g_{*} is within a reasonable range. We also derive a sizeindependent upper bound on the entropy density of a stiff fluid in terms of the energy density.
 Publication:

Physical Review D
 Pub Date:
 October 2006
 DOI:
 10.1103/PhysRevD.74.084004
 arXiv:
 arXiv:grqc/0609055
 Bibcode:
 2006PhRvD..74h4004H
 Keywords:

 04.70.Dy;
 04.20.Dw;
 04.70.Bw;
 Quantum aspects of black holes evaporation thermodynamics;
 Singularities and cosmic censorship;
 Classical black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Theory
 EPrint:
 4 pages, accepted for publication in Physical Review D, minor correction