Shock waves in Lifshitz-like spacetimes

We construct shock waves for Lifshitz-like geometries in four- and five-dimensional effective theories as well as in D3-D7 and D4-D6 brane systems. The solutions to the domain wall profile equations are found. Further, the study makes a connection with the implications for the quark-gluon plasma formation in heavy-ion collisions. According to the holographic approach, the multiplicity of particles produced in heavy-ion collisions can be estimated by the area of the trapped surface formed in shock wave collisions. We calculate the areas of trapped surfaces in the geometry of two colliding Lifshitz domain walls. Our estimates show that for five-dimensional cases with certain values of the critical exponent the dependence of multiplicity on the energy of colliding ions is rather close to the experimental data ${\cal M} \sim s^{\,0.15}$ observed at RHIC and LHC.Comment: 35 pages, 6 figures; v3: typos corrected. Version to appear in JHE

Exact solutions in gravity with a sigma model source

We consider a D-dimensional model of gravity with non-linear "scalar fields" as a matter source. The model is defined on the product manifold M, which contains n Einstein factor spaces. General cosmological type solutions to the field equations are obtained when n-1 factor spaces are Ricci-flat, e.g. when one space M_1 of dimension d_1 > 1 has nonzero scalar curvature. The solutions are defined up to solutions to geodesic equations corresponding to a sigma model target space. Several examples of sigma models are presented. A subclass of spherically-symmetric solutions is studied and a restricted version of "no-hair theorem" for black holes is proved. For the case d_1 =2 a subclass of latent soliton solutions is singled out.Comment: 22 pages, Latex, several phrases and 4 refs. are addes, few typos are eliminate

Elliptic solutions of generalized Brans-Dicke gravity with a non-universal coupling

We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma-model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansion. We also derive an analytical approximation in exponential functions.Comment: 24 pages, 3 figures; v2: typos fixed, few remarks and references added; version to appear in EPJ

Analytic black branes in Lifshitz-like backgrounds and thermalization

Using black brane solutions in 5d Lifshitz-like backgrounds with arbitrary dynamical exponent $\nu$, we construct the Vaidya geometry, asymptoting to the Lifshitz-like spacetime, which represents a thin shell infalling at the speed of light. We apply the new Lifshitz-Vaidya background to study the thermalization process of the quark-gluon plasma via the thin shell approach previously successfully used in several backgrounds. We find that the thermalization depends on the chosen direction because of the spatial anisotropy. The plasma thermalizes thus faster in the transversal direction than in the longitudinal one. To probe the system described by the Lifshitz-like backgrounds, we also calculate the holographic entanglement entropy for the subsystems delineated along both transversal and longitudinal directions. We show that the entropy has some universality in the behavior for both subsystems. At the same time, we find that certain characteristics strongly depend on the critical exponent $\nu$.Comment: 39 pages, 23 figures; v3: typos corrected, references and clarifications added, version published in JHE

Thermalization of holographic Wilson loops in spacetimes with spatial anisotropy

In this paper, we study behaviour of Wilson loops in the boost-invariant nonequilibrium anisotropic quark-gluon plasma produced in heavy-ion collisions within the holographic approach. We describe the thermalization studying the evolution of the Vaidya metric in the boost-invariant and spatially anisotropic background. To probe the system during this process we calculate rectangular Wilson loops oriented in different spatial directions. We find that anisotropic effects are more visible for the Wilson loops lying in the transversal plane unlike the Wilson loops with partially longitudinal orientation. In particular, we observe that the Wilson loops can thermalizes first unlike to the order of the isotropic model. We see that Wilson loops on transversal contours have the shortest thermalization time. We also calculate the string tension and the pseudopotential at different temperatures for the static quark-gluon plasma. We show that the pseudopotential related to the configuration on the transversal plane has the screened Cornell form. We also show that the jet-quenching parameter related with the average of the light-like Wilson loop exhibits the dependence on orientations.Comment: 39 pages, 12 figures; v3: typos corrected, to appear in Nucl. Phys.

Probing the holographic model of N=4\mathcal{N} =4 SYM rotating quark-gluon plasma

We study Wilson loops in holographic duals of the $\mathcal{N}=4$ SYM quark-gluon plasma. For this we consider the Schwarzschild-$AdS_5$ and Kerr-$AdS_5$ black holes, which are dual to the non-rotating and rotating QGPs, correspondingly. From temporal Wilson loops we find the heavy quark potentials in both backgrounds. For the temperature above the critical temperature we observe the Coulomb-like behavior of the potentials. We find that increasing the rotation the interquark distance decreases, we also see that the increase of the temperature yields the similar behavior. Moreover, at high temperatures for certain values of parameters the potentials in Schwarzschild-$AdS_5$ and Kerr-$AdS_5$ are close to that one calculated in the AdS black brane with a planar horizon. We also explore holographic light-like Wilson-loops from which the jet-quenching parameters of a fast parton are extracted. We find that the rotation increases the value of the jet-quenching parameter. However, at high temperatures the jet-quenching parameters have a cubic dependence on the temperature as for the the AdS black brane.Comment: 32 pp, 11 fig

Stability analysis of holographic RG flows in 3d supergravity

We study holographic RG flows in a 3d supergravity model from the side of the dynamical system theory. The gravity equations of motion are reduced to an autonomous dynamical system. Then we find equilibrium points of the system and analyze them for stability. We also restore asymptotic solutions near the critical points. We find two types of solutions: with asymptotically AdS metrics and hyperscaling violating metrics. We write down possible RG flows between an unstable (saddle) UV fixed point and a stable (stable node) IR fixed point. We also analyze bifurcations in the model.Comment: 26 pp., 7 figure

Holographic Wilson Loops in the Confining Backgrounds at Zero Temperature

We study Wilson loops in the exact renormalization group ow at zero tempera- ture via the 5d holographic model that reproduces the behavior of the QCD running coupling. Calculating the time-like rectangular Wilson loop we show that the model includes a conning phase at T = 0 in the IR region