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In this paper we consider the particular time-dependent background in five dimensions. We have used dual geometry in Eddington–Finkelstain type coordinates. By using the first law of black hole in AdS\(_5\) geometry, we obtain a thermodynamics formulation. Also we obtain the dynamical surface gravity for AdS\(_5\) black hole. We show that the first law of black hole dynamics needs some correction term.

abstract

The horizon hypothesis of quantum cosmology was put forward previously to justify the derivation of the Wheeler–DeWitt equation for the wave function of the Universe \({\mit \Psi }\) in the mini-superspace, assuming the Friedmann line element \(ds^2=dt^2-a^2(t)d\mathbf {x}^2\), when the three-space \(d\mathbf {x}^2\) is flat, by imposing a cut-off on spatial integrals at the causal horizon \(\xi ^{-1}(t)\equiv \left \{d\,[\ln {a(t)}]\,/dt\right \}^{-1}\). If the theory is defined by a Lagrangian \(L\) which includes higher-derivative gravitational terms \({\mathcal R}^2\), the resulting Schrödinger equation contains a potential that is constant in the case of cosmic dust, and after Wick rotation of the comoving time coordinate, \(t \rightarrow - i \tau \), the solution for \({\mit \Psi }\) takes the form of a Boltzmann distribution, from which it is possible to ascribe a finite temperature \(T\equiv \lambda \)/\(\tau \) to the dust, where the parameter \(\lambda \) subsumes the details of the cut-off, and which can be understood from the Heisenberg time-energy indeterminacy principle \(\Delta t\Delta E \sim \hbar \) applied to the observable Universe. Recently, Cai et al. have shown that the apparent horizon \(\tilde {r}_{\rm a}\) in Friedmann cosmology possesses thermal characteristics, associated with a temperature \(T=1\)/\(2\pi \tilde {r}_{\rm a}\) when measured by a Kodama observer comoving with the horizon. This result thus vindicates the horizon hypothesis, and leads to the exact value \(\lambda =3\pi \)/\(2\). The infra-red cut-off at the apparent horizon applies to all quantum field theoretical phenomena, and the inclusion of length scales that lie only inside the horizon is equivalent to the inclusion only of length scales lying outside their Schwarzschild radius, as conjectured by Cohen et al. , following earlier speculation by ’t Hooft. Analogies with the theory of superfluidity are also discussed.

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In this article, the peculiar context of sequential measurements is chosen in order to analyze the quantum specificity in the two most famous examples of Heisenberg and Bell inequalities: Results are found at some interesting variance with customary textbook materials, where the context of initial state re-initialization is described. A key-point of the analysis is the possibility of defining Joint Probability Distributions for sequential random variables associated to quantum operators. Within the sequential context, it is shown that Joint Probability Distributions can be defined in situations where not all of the quantum operators (corresponding to random variables) do commute two by two.

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A simple smooth chaotic system, which showed a 3-layer sphere chaotic attractor, is investigated. It is found that this chaotic attractor is a limit cycle instead of chaotic attractor. This situation was caused by the simulation time which is too short to reach its real status. It also shows that it is not reliable to construct chaotic system based only on the Šhilnikov criterion without finding the exact homoclinic orbits. Then a chaotic system with the real sphere shape is proposed. This proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagrams and Poincaré section.

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We consider the long-time behaviour of spherically symmetric solutions in the Einstein–Skyrme model. Using \(nonlinear\) perturbation analysis we obtain the leading order estimation of the tail in the topologically trivial sector (\(B=0\)) of the model. We show that solutions starting from small compactly supported initial data decay as \(t^{-4}\) at future timelike infinity and as \(u^{-2}\) at future null infinity. We also verified that long-time behaviour for the tail in Einstein–Skyrme model is exactly the same as it was obtained for wave maps.

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Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose–Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach’s principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon’s mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions.

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The ALICE and CMS data on the multiplicity distributions are compared with the lower energy data and with the results from the 8.142 version of the PYTHIA MC event generator with two tunings. The ALICE data for moments are used to calculate the factorial cumulants. It is suggested that the data on moments or cumulants are well suited to specify the optimal tuning of the model parameters.

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Evidence for the energy threshold of creating the quark-gluon plasma in nucleus–nucleus collisions, the so-called onset of deconfinement, has been found by the energy scan program of the NA49 experiment at the CERN SPS. In this paper we review the experimental and theoretical status of this phenomenon. First, the basic, qualitative ideas are presented for non-experts. Next, the latest experimental results are compared to a statistical model within which the onset of deconfinement and its signals had been predicted. Finally, alternative interpretations and open questions are discussed.

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Classical and relativistic multiphase and multicomponent flows represent an interesting field of research due to their various applications. In order to simulate multiphase and multicomponent flows, the effect due to interfaces between constituents has to be analyzed. In the approach following in this paper, the constituents are averaged to lead to a homogeneous mixture, thus only one set of equations for the total mass, momentum, and energy of the mixture, supplemented by equations for the mass or volume fraction of the constituents has to be solved. The main purpose of this paper is to develop the relativistic generalization of a recent classical approach to the study of multiphase and multicomponent homogeneous mixture. An hyperbolic system of equations is founded, made by particle number and energy-tensor conservations equations, supplemented by mass or volume fraction equations for the constituents. Thus, a non linear wave propagation compatible with this system is considered.