Abstract
We discuss a general five-dimensional completely anisotropic holographic model with three different spatial scale factors, characterized by a Van der Waals-like phase transition between small and large black holes. A peculiar feature of the model is the relation between anisotropy of the background and anisotropy of the colliding heavy ions geometry. We calculate the holographic entanglement entropy (HEE) of the slab-shaped region, the orientation of which relatively to the beams line and the impact parameter is characterized by the Euler angles. We study the dependences of the HEE and its density on the thermodynamic (temperature, chemical potential) and geometric (parameters of anisotropy, thickness, and orientation of entangled regions) parameters. As a particular case the model with two equal transversal scaling factors is considered. This model is supported by the dilaton and two Maxwell fields. In this case we discuss the HEE and its density in detail: interesting features of this model are jumps of the entanglement entropy and its density near the line of the small/large black hole phase transition. These jumps depend on the anisotropy parameter, chemical potential, and orientation. We also discuss different definitions and behavior of c-functions in this model. The c-function calculated in the Einstein frame decreases while ℓ is increasing for all ℓ in the isotropic case (in regions of (μ, T )-plane far away from the line of the phase transition). We find the non-monotonicity of the c-functions for several anisotropic configurations, which however does not contradict with any of the existing c-theorems since they all are based on Lorentz invariance.
Highlights
IntroductionFundamental questions addressed in studies of high energy heavy ions collisions (HIC) at RHIC and LHC, and future experiments NICA and FAIR, concern understanding of quark-gluon plasma (QGP) formation, i.e. thermalization of media produced in HIC, thermodynamic entropy production, and its characteristics such as quantum entanglement, decoherence etc
We study the dependences of the holographic entanglement entropy (HEE) and its density on the thermodynamic and geometric parameters
Fundamental questions addressed in studies of high energy heavy ions collisions (HIC) at RHIC and LHC, and future experiments NICA and FAIR, concern understanding of quark-gluon plasma (QGP) formation, i.e. thermalization of media produced in HIC, thermodynamic entropy production, and its characteristics such as quantum entanglement, decoherence etc
Summary
Fundamental questions addressed in studies of high energy heavy ions collisions (HIC) at RHIC and LHC, and future experiments NICA and FAIR, concern understanding of quark-gluon plasma (QGP) formation, i.e. thermalization of media produced in HIC, thermodynamic entropy production, and its characteristics such as quantum entanglement, decoherence etc. The HEE during thermalization usually evolves to the thermal entanglement entropy [31,32,33,34,35,36,37,38,39,40,41,42] With this approach, there is a natural possibility of studying the evolution of entropy in HIC (thermalization) and phase transitions for the obtained thermal media in the framework of the same holographic model. We start with the most general anisotropic holographic model and consider the general orientation of the slab-shaped entangled region with respect to the geometry of HIC. We end the paper with the conclusion and discussion of future directions of research on the subject
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