Black Hole Thermodynamics and the Factor of 2 Problem

TL;DR

This paper demonstrates that tunneling formulas for black hole radiation naturally follow from thermodynamics principles, addressing the factor of 2 problem by linking radiation temperature discrepancies to invariant tunneling expressions.

Contribution

It shows that recent tunneling formulas are derived from the first law of thermodynamics and the area-entropy relation, clarifying the factor of 2 issue in black hole radiation.

Findings

Tunneling formulas follow from thermodynamics principles.

A higher radiation temperature leads to a canonically invariant tunneling formula.

Addresses the factor of 2 problem in black hole radiation theories.

Abstract

We show that the recent tunneling formulas for black hole radiation in static, spherically symmetric spacetimes follow as a consequence of the first law of black hole thermodynamics and the area-entropy relation based on the radiation temperature. A tunneling formula results even if the radiation temperature is different from the one originally derived by Hawking and this is discussed in the context of the recent factor of 2 problem. In particular, it is shown that if the radiation temperature is higher than the Hawking temperature by a factor of two, thermodynamics then leads to a tunneling formula which is exactly the one recently found to be canonically invariant.