Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy

Abstract

Several investigations show that in a very small length scale there exists corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket among the charges is calculated. We show that the Fourier modes of the bracket is exactly similar to Virasoro algebra. Then using Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for entropy; i.e. the Bekenstein-Hawking form, is not modified.

Minor modifications, to appear in EPJC

References in corpus (6)

• Quantum Tunneling and Back Reaction
• Fermion Tunneling Beyond Semiclassical Approximation
• Quantum Tunneling and Trace Anomaly
• Macroscopic Effects of the Quantum Trace Anomaly
• Lessons from Classical Gravity about the Quantum Structure of Spacetime
• Towards thermodynamics of universal horizons in Einstein-æther theory

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• Near horizon hidden symmetry and entropy of Sultana-Dyer black hole: A time dependent case
• Symmetries near a generic charged null surface and associated algebra: an off-shell analysis
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Near horizon symmetry and entropy of black holes in $f(R)$ gravity and conformal gravity
• The boundary effect of anomaly-induced action
• Diffeomorphism symmetries near a timelike surface in black hole spacetime
• BMS Goldstone modes near the horizon of a Kerr black hole are thermal