Entanglement Entropy of Two Black Holes and Entanglement Entropic Force

G. ’t Hooft, Nucl. Phys. B256, 727 (1985)

1985

Earlier work this paper cites.

L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, Phys. Rev. D34, 373 (1986)

1986

Earlier work this paper cites.

M. Srednicki, Phys. Rev. Lett. 71, 666 (1993), arXiv:hep-th/9303048

1993

Earlier work this paper cites.

V. P. Frolov and I. Novikov, Phys. Rev. D48, 4545 (1993), arXiv:gr-qc/9309001

1993

Earlier work this paper cites.

L. Susskind and J. Uglum, Phys. Rev. D50, 2700 (1994), arXiv:hep-th/9401070

1994

Earlier work this paper cites.

T. Jacobson, (1994), arXiv:gr-qc/9404039

1994

Cited alongside, same era.

C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B424, 443 (1994), arXiv:hep-th/9403108

1994

Cited alongside, same era.

D. N. Kabat, Nucl. Phys. B453, 281 (1995), arXiv:hep-th/9503016

1995

Cited alongside, same era.

M. Nielsen and I. Chuang, Cambridge University Press, Cambridge, UK 3, 9 (2000)

2000

Cited alongside, same era.

S. Hawking, J. M. Maldacena, and A. Strominger, JHEP 05, 001 (2001), arXiv:hep- th/0002145

2001

Cited alongside, same era.

When d=1, this is not correct because generally the correlation function ⟨ 0 | ​ ϕ ​ ( t , x ) ​ ϕ ​ ( t , y ) ​ | 0 ⟩ \bra{0}\phi(t,x)\phi(t,y)\ket{0} does not become zero when | x − y | → ∞ |x-y|\rightarrow\infty . For example the correlation function of massless free scalar fields does not become zero when | x − y | → ∞ |x-y|\rightarrow\infty

Cited in the paper.

We use the following easily verifiable identity, ( A C D B ) = ( A − C ​ B − 1 ​ D C ​ B − 1 0 1 ) ​ ( 1 0 D B ) = ( A 0 D 1 ) ​ ( 1 A − 1 ​ C 0 B − D ​ A − 1 ​ C ) . \begin{pmatrix}A&C\\ D&B\end{pmatrix}=\begin{pmatrix}A-CB^{-1}D&CB^{-1}\\ 0&1\end{pmatrix}\begin{pmatrix}1&0\\ D&B\end{pmatrix}=\begin{pmatrix}A&0\\ D&1\end{pmatrix}\begin{pmatrix}1&A^{-1}C\\ 0&B-DA^{-1}C\end{pmatrix}

Original

Cited in the paper.

P. Calabrese and J. L. Cardy, J. Stat. Mech. 0406, P002 (2004), arXiv:hep-th/0405152

2004

Later among the works it cites.

S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006), arXiv:hep-th/0603001

2006

Later among the works it cites.

S. Ryu and T. Takayanagi, JHEP 08, 045 (2006), arXiv:hep-th/0605073

2006

Later among the works it cites.

T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Phys. Rev. Lett. 99, 170403 (2007), arXiv:0707.1862 [cond-mat.stat-mech]

Original

2007

Later among the works it cites.

H. Casini and M. Huerta, J. Phys. A42, 504007 (2009), arXiv:0905.2562 [hep-th]

Original

2009

Later among the works it cites.