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

TL;DR

This paper demonstrates a smooth transition from classical gravitational entropy of a collapsing star to quantum black hole entropy, emphasizing the geometric origin of Bekenstein-Hawking entropy independent of matter details.

Contribution

It introduces a robust mechanism showing the geometric origin of black hole entropy during collapse and evaporation, bridging classical and quantum regimes without dependence on interior matter dynamics.

Findings

Entropy transitions smoothly at horizon formation

Both regimes involve Vaidya exterior radiation

Bekenstein-Hawking entropy arises from geometry

Abstract

We present a robust mechanism where the geometrical free-gravitational entropy of an isolated astrophysical radiating star undergoing continual gravitational collapse, 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 regime and the semi classical evaporating black hole regime, the matter is radiated via the Vaidya exterior surrounding the radiating star, as well as the evaporating black hole. 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.