Built on

G. ’t Hooft, “Dimensional reduction in quantum gravity,” [arXiv:gr-qc/9310026]; L. Susskind, “The World as a hologram,” J. Math. Phys. 36
1995
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
V. Balasubramanian and P. Kraus, “A Stress tensor for Anti-de Sitter gravity,” Commun. Math. Phys. 208
2001
Earlier work this paper cites.
P. K. Kovtun and A. O. Starinets, “Quasinormal modes and holography,” Phys. Rev. D 72
2005
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
D. V. Fursaev, “Proof of the holographic formula for entanglement entropy,” JHEP 0609
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
Earlier work this paper cites.

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2013

Entropic Counterpart of Perturbative Einstein Equation

Bhattacharya, Jyotirmoy, Takayanagi, Tadashi

Understand

Entanglement entropy in a field theory, with a holographic dual, may be viewed as a quantity which encodes the diffeomorphism invariant bulk gravity dynamics.

This, in particular, indicates that the bulk Einstein equations would imply some constraints for the boundary entanglement entropy.
In this paper we focus on the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and analyze the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state.
Specifically, we consider linear fluctuations about BTZ black hole in 3 dimension, pure AdS and AdS Schwarzschild black holes in 4 dimensions and obtain a diffeomorphism invariant reformulation of linearized Einstein equation in terms of holographic entanglement entropy.

Built on

G. ’t Hooft, “Dimensional reduction in quantum gravity,” [arXiv:gr-qc/9310026]; L. Susskind, “The World as a hologram,” J. Math. Phys. 36
1995
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428
1998
Earlier work this paper cites.
J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1999
Earlier work this paper cites.
V. Balasubramanian and P. Kraus, “A Stress tensor for Anti-de Sitter gravity,” Commun. Math. Phys. 208
2001
Earlier work this paper cites.
P. K. Kovtun and A. O. Starinets, “Quasinormal modes and holography,” Phys. Rev. D 72
2005
Earlier work this paper cites.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
D. V. Fursaev, “Proof of the holographic formula for entanglement entropy,” JHEP 0609
2006
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
Earlier work this paper cites.