Holographic Entanglement Entropy For Black Strings

The holographic principle has be one of the most fundamental principles in physics.AdS/CFT duality is a concrete realization of the holographic principle,it means that a d+2 dimensional AdS space(AdSd+2)to d+1 dimensional CFT(CFTd+1),which is sitting at the boundary of the AdSd+2,AdS/CFT duality play an important role in connecting conformal field theories with gravitational theories.The holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence.In this paper,we focus on the study of the holographic entanglement entropy(HEE)for 4-dimensional sylindrically symmetric and asymptotically AdS black hole-black strings.First of all,we brief introduce the quantum entanglement and entanglement entropy,holographic principle and AdS/CFT correspondence and it's application.After that,we briefly review several initial model of holographical entanglemen-t entropy,such as the HEE for simplest AdS3/CFT2 in global coordinate and Poincare coordinate,the HEE for BTZ black hole at a finite temperature,entan-glement entropy in CFTd+1 from AdS d+2.Some of theoretical approaches and calculative process have been followed by the later generation.When the boundary locating at infinite radial coordinate,we investigate the HEE of 4-dimensional sylindrically symmetric black strings by using Ryu-Takayanagi formula.It is shown that,with the infinity boundary,the zero-order contribution of the HEE is divergent and it comes from the AdS background when using perturbatiol expansion up to(?/?0)3 order.If we remove this contribution,the remaining part is finite and proportional to the ADM mass M.For charged black string,the the mass-term contribution to the HEE is the same with the neutral case,and the charged-term contribution is negative.For 4-dimensional sylindrically symmetric and asymptotically AdS spacetime-black strings,as taking the boundary near the horizon,we find that the HEE is finite and proportional to the area of the subsystem when we perturbatively expand the minimal surface into second order.The HEE equals the Bekenstein-Hawking entropy if the subsystem covers the whole conformal boundary,for both charged and uncharged cases.In particular,the minimal surface(Ryu-Takayanagi surface)always stays in the bulk region for uncharged and non-extremal charged cases,while it is immersed inside the boundary for extremal black string.It's worth mentioning that we also present the numerical results according to the initial equation of motion.We can see that the perturbative results agree with the numerical solutions.We give a summary and a outlook of holographic entanglement entropy in the end.