Abstract
The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane. On the boundary, we calculated the regularized HEE of a disk region of different sizes. We find strong numerical evidence for the failure of equal area law for isobaric curves on the temperature-HEE plane and for the correctness of first law of entanglement entropy, and briefly give an explanation for why the latter may serve as a reason for the former, i.e. the failure of equal area law on the temperature-HEE plane.
Highlights
JHEP09(2016)060 results show that for RN-AdS black holes this “equal area law” on the HEE-temperature curve holds up to an accuracy of around 1%, it fails for dyonic RN-AdS black holes
On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane
Motivated by the above considerations and progresses, we extended the study of van der Waals-like behavior for HEE to Gauss-Bonnet AdS black holes with a spherical horizon in (4+1)-dimensions
Summary
We give a brief review of the thermodynamics of Gauss-Bonnet AdS Black holes. [40], the Maxwell’s equal area law for Gauss-Bonnet AdS black holes is studied on the P − V plane. There is an intersection point at T = T ∗ < Tc on the isobaric Gibbs free energy versus temperature curve, which implies that at this temperature the small black hole may jump into a large black hole This is a first order phase transition similar to the phase transition studied in the P − V plane. When P = Pc, there is an inflection point on the isobaric curve, and the area of both closed regions mentioned shrinks to zero In this case, the size of the three black holes at the same temperature becomes identical, and the phase transition becomes continuous and is of the second order. If the pressure P increases further so that P > Pc holds, T becomes a monotonous function of S, and there can be only a single black hole at each temperature, the phase transition no longer occurs
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