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

The European Physical Journal C

Sumanta Chakraborty¹  Bibhas Ranjan Majhi² 

[1] IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007, Pune, India;IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007, Pune, India;Racah Institute of Physics, Hebrew University of Jerusalem, Givat Ram, 91904 , Jerusalem, Israel;

关键词: Entropy;    Black Hole;    Fourier Mode;    Virasoro Algebra;    Trace Anomaly;   

DOI  :  10.1140/epjc/s10052-014-2867-6

来源: Springer

【 摘 要 】

Several investigations show that in a very small length scale there exist 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 for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the 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 the entropy; i.e. the Bekenstein–Hawking form, is not modified.

【 授权许可】

CC BY