Third potential evidence for the new area spectrum based on the Einstein-Kaufman pseudo tensor, a conjecture

TL;DR

This paper proposes a conjecture for a mathematical formula related to the new area spectrum based on the Einstein-Kaufman pseudo tensor, extending previous evidence for its validity in black hole entropy and radiation spectrum.

Contribution

It introduces a conjectural mathematical formula that approximates a constant related to the new area spectrum, building on prior numerical evidence.

Findings

Proposes a formula estimating the constant around 172.8

Provides a third potential numerical evidence for the new spectrum

Builds on earlier results matching Bekenstein-Hawking entropy and Hawking radiation

Abstract

This paper has been withdrawn by the authors. 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 potential, albeit not 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$\sim$173 by fitting it to the Planck radiation spectrum. In this article, we propose a mathematical formula that reproduces this value. According to this formula, this constant is around 172.8. Nevertheless, we failed to concretely derive this mathematical formula. Therefore, it is a conjecture.