Logarithmic correction to BH entropy as Noether charge

Understand

We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equation in four dimensions.

• Via Wald's Noether charge formalism, we compute the contribution to the entropy coming from the anomaly induced effective action and unveil a logarithmic correction to the Bekenstein-Hawking area law.
• The corrected entropy is given by a seemingly universal formula involving the coefficient of the type-A trace anomaly, the Euler characteristic of the horizon and the value at the horizon of the solution to the uniformization problem for Q-curvature.
• Two instances are examined in detail: Schwarzschild and a four-dimensional massless topological black hole.