Black Hole Entropy Prediction without Immirzi Parameter

TL;DR

This paper provides numerical evidence supporting a new black hole area spectrum that reproduces entropy without the Immirzi parameter, confirming previous results with an independently calculated constant value.

Contribution

It introduces a new method to calculate the constant in the area spectrum, reinforcing the validity of the spectrum without fixing the Immirzi parameter.

Findings

Constant value approximately 172.87 supports the new spectrum

Reproduces Bekenstein-Hawking entropy without Immirzi parameter

Consistent with earlier fitting results

Abstract

In our earlier paper "Corrections to the Bekenstein-Hawking entropy and the Hawking radiation spectrum", arXiv:0910.2755, we provided two concrete numerical evidences for the new area spectrum based on the Einstein-Kaufman pseudo tensor as opposed to the Ashtekar variables: namely, the reproduction of the Bekenstein-Hawking entropy without fixing Immirzi parameter and the reproduction of the Hawking radiation spectrum. In this article, we provide another concrete, numerical evidence for this new area spectrum; there was a constant in our earlier article, which was inversely proportional to the density of state, and which we could not fix a priori. Nevertheless, in our earlier article, we obtained this constant to be around 172~173 by fitting it to the Planck radiation spectrum. In this article, we calculate this value using another method. We obtain 172.87...which implies consistency.