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Logarithmic correction to BH entropy as Noether charge

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Abstract

We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equations 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

$$ {S_{\text{bh}}} = \frac{{{\mathcal{A}_\mathcal{H}}}}{4} - a \cdot {\mathcal{X}_\mathcal{H}} \cdot {\phi_\mathcal{H}} $$

involving the coefficient a of the type-A trace anomaly, the Euler characteristic \( {\mathcal{X}_\mathcal{H}} \) of the horizon and the value at the horizon \( {\phi_\mathcal{H}} \) 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. We also find agreement with the logarithmic correction due to one-loop contribution of conformal fields in the Schwarzschild background.

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  1. Universidad Andrés Bello, Departamento de Ciencias Físicas, República 220, Santiago, Chile

    R. Aros, D.E. Díaz & A. Montecinos

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  1. R. Aros
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  2. D.E. Díaz
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  3. A. Montecinos
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Correspondence to D.E. Díaz.

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ArXiv ePrint: 1003.1083

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Aros, R., Díaz, D. & Montecinos, A. Logarithmic correction to BH entropy as Noether charge. J. High Energ. Phys. 2010, 12 (2010). https://doi.org/10.1007/JHEP07(2010)012

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