Black quanta. On the thermodynamics of the black holes - M Apostol (Annals of Mathematics and Physics - Peertechz Publications, 2019)
It is well known that bodies may suffer a gravitational collapse, providing their mass is suffi ciently large, their dimensions are suffi ciently small and their measurable internal motion ceased [1,2]. In such a state they are black holes. We cannot have any information about their internal state. Any mass or radiation signal falls in the infi nite spacetime singularity of the black holes. In order to get a qualitative criterion of the black-hole condition we use GM2 / R for the gravitational energy of a spherical mass M with radius R , where G 6.7  108cm3 / g  s is the gravitational constant; if GM2 / R > Mc2 (where c  3  1010cm/ s is the speed of light in vacuum), i.e. if M / R > c2 / G , the mass collapses; the condition may also be written as R < Rh , where Rh = GM / c2 is close to the Schwarzschild radius rh = 2Rh . We take Rh = GM / c2 as the radius of any black hole with mass M .