TY - JOUR

T1 - First law of entanglement entropy in AdS black hole backgrounds

AU - Ishibashi, Akihiro

AU - Maeda, Kengo

N1 - Funding Information:
We would like to thank Takashi Okamura for useful discussions. This work was supported in part by JSPS KAKENHI Grants No. 17K05451, No. 20K03975 (K. M.) and No. 15K05092, No. 20K03938 (A. I.).
Publisher Copyright:
© 2021 authors. Published by the American Physical Society.

PY - 2021/7/15

Y1 - 2021/7/15

N2 - The first law for entanglement entropy in CFT in an odd-dimensional asymptotically AdS black hole is studied by using the AdS/CFT duality. The entropy of CFT considered here is due to the entanglement between two subsystems separated by the horizon of the AdS black hole, which itself is realized as the conformal boundary of a black droplet in even-dimensional global AdS bulk spacetime. In (2+1)-dimensional CFT, the first law is shown to be always satisfied by analyzing a class of metric perturbations of the exact solution of a 4-dimensional black droplet. In (4+1)-dimensions, the first law for CFT is shown to hold under the Neumann boundary condition at a certain bulk hypersurface anchored to the conformal boundary of the boundary AdS black hole. From the boundary view point, this Neumann condition yields there being no energy flux across the boundary of the boundary AdS black hole. Furthermore, the asymptotic geometry of a 6-dimensional small AdS black droplet is constructed as the gravity dual of our (4+1)-dimensional CFT, which exhibits a negative energy near the spatial infinity, as expected from vacuum polarization.

AB - The first law for entanglement entropy in CFT in an odd-dimensional asymptotically AdS black hole is studied by using the AdS/CFT duality. The entropy of CFT considered here is due to the entanglement between two subsystems separated by the horizon of the AdS black hole, which itself is realized as the conformal boundary of a black droplet in even-dimensional global AdS bulk spacetime. In (2+1)-dimensional CFT, the first law is shown to be always satisfied by analyzing a class of metric perturbations of the exact solution of a 4-dimensional black droplet. In (4+1)-dimensions, the first law for CFT is shown to hold under the Neumann boundary condition at a certain bulk hypersurface anchored to the conformal boundary of the boundary AdS black hole. From the boundary view point, this Neumann condition yields there being no energy flux across the boundary of the boundary AdS black hole. Furthermore, the asymptotic geometry of a 6-dimensional small AdS black droplet is constructed as the gravity dual of our (4+1)-dimensional CFT, which exhibits a negative energy near the spatial infinity, as expected from vacuum polarization.

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U2 - 10.1103/PhysRevD.104.026004

DO - 10.1103/PhysRevD.104.026004

M3 - Article

AN - SCOPUS:85110402829

VL - 104

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 2

M1 - 026004

ER -