Information-carrying Hawking radiation and the number of microstate for a black hole

TL;DR

This paper establishes a criterion to determine if Hawking radiation is unitary, enabling calculation of black hole microstates and entropy from radiation spectra, and confirms consistency with string theory for extremal Reissner-Nordström black holes.

Contribution

It introduces a condition to verify unitarity in Hawking radiation and calculates black hole microstates directly from radiation spectra, aligning with string theory results.

Findings

Derived a criterion to falsify unitarity in Hawking radiation spectra.

Calculated Bekenstein-Hawking entropies from radiation microstates.

Confirmed consistency with string theory for extremal Reissner-Nordström black holes.

Abstract

We present a necessary and sufficient condition to falsify whether a Hawking radiation spectrum indicates unitary emission process or not from the perspective of information theory. With this condition, we show the precise values of Bekenstein-Hawking entropies for Schwarzschild black holes and Reissner-Nordstr\"om black holes can be calculated by counting the microstates of their Hawking radiations. In particular, for the extremal Reissner-Nordstr\"om black hole, its number of microstate and the corresponding entropy we obtain are found to be consistent with the string theory results. Our finding helps to refute the dispute about the Bekenstein-Hawking entropy of extremal black holes in the semiclassical limit.