Gravitational anomalies and one dimensional behaviour of black holes

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.

Comments added, to appear in EPJC

References in corpus (8)

• Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies
• Quantum Tunneling and Trace Anomaly
• Hawking Radiation and Covariant Anomalies
• Hawking Radiation, Covariant Boundary Conditions and Vacuum States
• Gravitational anomalies and entropy
• Dimension of quantum channel of radiation in pure Lovelock black holes
• Connection between response parameter and anomaly coefficient in two dimensional anomalous fluid
• Vacuum condition and the relation between response parameter and anomaly coefficient in (1+3) dimensions

Cited by in corpus (2)

• Microscopic derivation of the Bekenstein-Hawking entropy for Schwarzschild black holes
• A note on entropy of matter in presence of gravity: status of extensivity of entropy