language: en

Power-law corrections to entanglement entropy of horizons

Saurya Das, 1, * S. Shankaranarayanan, 2,? and Sourav Sur 1,?
1 Department of Physics, University of Lethbridge,
4401 University Drive, Lethbridge, Alberta, Canada T1K 3M4
2 Max-Planck-Institut für Gravitationphysik,
Am Mühlenberg 1, D-14476 Potsdam, Germany
(Received 29 December 2007; published 10 March 2008)

We reexamine the idea that the origin of black-hole entropy may lie in the entanglement of quantum fields between the inside and outside of the horizon. Motivated by the observation that certain modes of gravitational fluctuations in a black-hole background behave as scalar fields, we compute the entanglement entropy of such a field, by tracing over its degrees of freedom inside a sphere. We show that while this entropy is proportional to the area of the sphere when the field is in its ground state, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. The area law is thus recovered for large areas. Further, we identify the location of the degrees of freedom that give rise to the above entropy.

DOI: 10.1103/PhysRevD.77.064013 PACS numbers: 04.60.-m, 04.70.-s, 04.70.Dy, 03.65.Ud

I. INTRODUCTION