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Advances in High Energy Physics
Volume 2015, Article ID 523408, 11 pages
http://dx.doi.org/10.1155/2015/523408
Research Article

Weak Minimal Area in Entanglement Entropy

1Department of Physics, Utkal University, Bhubaneswar 751004, India
2Centre of Excellence in Theoretical and Mathematical Sciences, Siksha ‘O’ Anusandhan University, Khandagiri Square, Bhubaneswar 751030, India

Received 18 November 2014; Accepted 8 February 2015

Academic Editor: Sally Seidel

Copyright © 2015 Shesansu Sekhar Pal and Shubhalaxmi Rath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We revisit the minimal area condition of Ryu-Takayanagi in the holographic calculation of the entanglement entropy, in particular, the Legendre test and the Jacobi test. The necessary condition for the weak minimality is checked via Legendre test and its sufficient nature via Jacobi test. We show for AdS black hole with a strip type entangling region that it is this minimality condition that makes the hypersurface unable to cross the horizon, which is in agreement with that studied earlier by Engelhardt et al. and Hubeny using a different approach. Moreover, demanding the weak minimality condition on the entanglement entropy functional with the higher derivative term puts a constraint on the Gauss-Bonnet coupling; that is, there should be an upper bound on the value of the coupling, .