Gravitational anomalies and one-dimensional behavior of black holes

It has been pointed out by Bekenstein and Mayo that the behavior of the black hole's entropy or information flow is similar to information flow through one-dimensional channel. Here I analyze the same issue with the use of gravitational anomalies. The rate of the entropy change (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 S^. on the power is S^. ∝P^1/2, which is identical to that for the information flow in a 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 the one-dimensional situation, known as Pendry's formula, while in the latter situation its value decreases