From a collapsing radiating star to an evaporating black hole: A smooth transition from classical to quantum entropy

Abstract We present a robust mechanism, where the geometrical free-gravitational entropy of an isolated astrophysical radiating star undergoing continual gravitational collapse (where gravity dominates over all other fundamental forces), as measured by an external observer, makes a smooth transition to the Bekenstein-Hawking entropy at the onset of the horizon formation and in the late times of black hole evaporation. It is interesting to note that both in the classical collapsing phase and the semi classical evaporating black hole phase, the matter is radiated via the Vaidya exterior that surrounds the collapsing radiating star as well as the evaporating black hole (BH) thus formed. As the entropy of a BH is several orders of magnitude greater than the ordinary thermodynamic entropy of the original star, so the BH entropy is basically independent of the nature of the interior matter. Therefore, our result, being independent of the interior matter dynamics of the collapsing star, clearly indicates that the Bekenstein-Hawking entropy and its non-extensive nature indeed originates from the Riemannian geometry, which dictates the free-gravity entropy in general relativity.