Gravitational anomalies and one dimensional behaviour of black holes

TL;DR

This paper demonstrates that black hole entropy and information flow behave like a one-dimensional system, using gravitational anomalies to analyze the relationship between entropy change and Hawking radiation power.

Contribution

It introduces a novel analysis of black hole information flow using gravitational anomalies, confirming the one-dimensional behavior in both 1+1 and 1+3 dimensions.

Findings

Entropy change scales as the square root of power, matching one-dimensional systems.

Proportionality constant in 1+1 dimensions equals Pendry's formula.

In 1+3 dimensions, the constant decreases, indicating a deviation from the ideal one-dimensional case.

Abstract

It has been pointed out by Bekenstein and Mayo that the behavior of the Black hole's entropy or information flow is similar to that through one-dimensional channel. Here I analyse the same issue with the use of gravitational anomalies. The rate of the entropy change ($\dot{S}$) and the power ($P$) of the Hawking emission are calculated from the relevant components of the anomalous stress-tensor under the Unruh vacuum condition. I show that the dependence of $\dot{S}$ on power is $\dot{S}\propto P^{1/2}$ which is identical to that for the information flow in one dimensional system. This is established by using the ($1+1$) dimensional gravitational anomalies first. Then the fact is further bolstered by considering the ($1+3$) dimensional gravitational anomalies. It is found that in the former case, the proportionality constant is exactly identical to one dimensional situation, known as Pendry's formula, while in later situation its value decreases.