Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock Gravity and the Counterterm Method

We generalize the quasilocal definition of the stress energy tensor of Einstein gravity to the case of third order Lovelock gravity, by introducing the surface terms that make the action well-defined. We also introduce the boundary counterterm that removes the divergences of the action and the conserved quantities of the solutions of third order Lovelock gravity with zero curvature boundary at constant $t$ and $r$. Then, we compute the charged rotating solutions of this theory in $n+1$ dimensions with a complete set of allowed rotation parameters. These charged rotating solutions present black hole solutions with two inner and outer event horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. We compute temperature, entropy, charge, electric potential, mass and angular momenta of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We find a Smarr-type formula and perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.Comment: 19 pages, 1 figure, a few references added, typos correcte

Thermodynamic Instability of Black Holes of Third Order Lovelock Gravity

In this paper, we compute the mass and the temperature of the uncharged black holes of third order Lovelock gravity and compute the entropy through the use of first law of thermodynamics. We perform a stability analysis by studying the curves of temperature versus the mass parameter, and find that there exists an intermediate thermodynamically unstable phase for black holes with hyperbolic horizon. The existence of this unstable phase for the uncharged topological black holes of third order Lovelock gravity does not occur in the lower order Lovelock gravity. We also perform a stability analysis for a spherical, 7-dimensional black hole of Lovelock gravity and find that while these kinds of black holes for small values of Lovelock coefficients have an intermediate unstable phase, they are stable for large values of Lovelock coefficients. We also find that there exists an intermediate unstable phase for these black holes in higher dimensions. This stability analysis shows that the thermodynamic stability of black holes with curved horizons is not a robust feature of all the generalized theories of gravity.Comment: 16 pages, 8 figure

Thermodynamics of Asymptotically Flat Charged Black Holes in Third Order Lovelock Gravity

We present a new class of asymptotically flat charge static solutions in third order Lovelock gravity. These solutions present black hole solutions with two inner and outer event horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. We find that the uncharged asymptotically flat solutions can present black hole with two inner and outer horizons. This kind of solution does not exist in Einstein or Gauss-Bonnet gravity, and it is a special effect in third order Lovelock gravity. We compute temperature, entropy, charge, electric potential and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We also perform a stability analysis by computing the determinant of Hessian matrix of the mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that there exists only an intermediate stable phase.Comment: 16 pages, two figures, a few references, and one sections added. Some properties of these new solutions which are different from Gauss-Bonnet gravity have been highlighte

Surface Terms of Quartic Quasitopological Gravity and Thermodynamics of Nonlinear Charged Rotating Black Branes

As in the case of Einstein or Lovelock gravity, the action of quartic quasitopological gravity has not a well-defined variational principle. In this paper, we first introduce a surface term that makes the variation of quartic quasitopological gravity well defined. Second, we present the static charged solutions of quartic quasitopological gravity in the presence of a non linear electromagnetic field. One of the branch of these solutions presents a black brane with one or two horizons or a naked singularity depending on the charge and mass of the solution. The thermodynamic of these black branes are investigated through the use of the Gibbs free energy. In order to do this, we calculate the finite action by use of the counterterm method inspired by AdS/CFT correspondence. Introducing a Smarr-type formula, we also show that the conserved and thermodynamics quantities of these solutions satisfy the first law of thermodynamics. Finally, we present the charged rotating black branes in $(n+1)$ dimensions with $k\leq [n/2]$ rotation parameters and investigate their thermodynamics.Comment: 16 pages, Late

Abelian Higgs Hair for a Static Charged Black String

We study the problem of vortex solutions in the background of an electrically charged black string. We show numerically that the Abelian Higgs field equations in the background of a four-dimensional black string have vortex solutions. These solutions which have axial symmetry, show that the black string can support the Abelian Higgs field as hair. This situation holds also in the case of the extremal black string. We also consider the self-gravity of the Abelian Higgs field and show that the effect of the vortex is to induce a deficit angle in the metric under consideration.Comment: REVTEX4, 12 pages, 6 figures, The version to be appeared in Phys. Rev.

Magnetic Branes in Gauss-Bonnet Gravity

We present two new classes of magnetic brane solutions in Einstein-Maxwell-Gauss-Bonnet gravity with a negative cosmological constant. The first class of solutions yields an $(n+1)$-dimensional spacetime with a longitudinal magnetic field generated by a static magnetic brane. We also generalize this solution to the case of spinning magnetic branes with one or more rotation parameters. We find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when all the rotation parameters are zero, the electric field vanishes, and therefore the brane has no net electric charge. For the spinning brane, when one or more rotation parameters are non zero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Again we find that the net electric charge of the branes in these spacetimes is proportional to the magnitude of the velocity of the brane. Finally, we use the counterterm method in the Gauss-Bonnet gravity and compute the conserved quantities of these spacetimes.Comment: 17 pages, No figure, The version to be published in Phys. Rev.

Spring search algorithm for simultaneous placement of distributed generation and capacitors

Purpose. In this paper, for simultaneous placement of distributed generation (DG) and capacitors, a new approach based on Spring Search Algorithm (SSA), is presented. This method is contained two stages using two sensitive index Sv and Ss. Sv and Ss are calculated according to nominal voltageand network losses. In the first stage, candidate buses are determined for installation DG and capacitors according to Sv and Ss. Then in the second stage, placement and sizing of distributed generation and capacitors are specified using SSA. The spring search algorithm is among the optimization algorithms developed by the idea of laws of nature and the search factors are a set of objects. The proposed algorithm is tested on 33-bus and 69-bus radial distribution networks. The test results indicate good performance of the proposed methodЦель. В статье для одновременного размещения распределенной генерации и конденсаторов представлен новый подход, основанный на "пружинном" алгоритме поиска (Spring Search Algorithm, SSA). Данный метод состоит из двух этапов с использованием двух показателей чувствительности Sv и Ss. Показатели чувствительности Sv и Ss рассчитываются в соответствии с номинальным напряжением и потерями в сети. На первом этапе определяются шины-кандидаты для установки распределенной генерации и конденсаторов согласно Sv и Ss. Затем, на втором этапе размещение и калибровка распределенной генерации и конденсаторов выполняются с использованием алгоритма SSA. "Пружинный" алгоритм поиска входит в число алгоритмов оптимизации, разработанных на основе идей законов природы, а факторы поиска представляют собой набор объектов. Предлагаемый алгоритм тестируется на радиальных распределительных сетях с 33 и 69 шинами. Результаты тестирования показывают хорошую эффективность предложенного метода

The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues

We investigate the dependence of the mechanical and hydraulic properties of poroelastic materials on the interstitial volume fraction (porosity) of the fluid flowing through their pores and compressibility of their elastic (matrix) phase. The mechanical behavior of the matrix is assumed of linear elastic type and we conduct a three-dimensional microstructural analysis by means of the asymptotic homogenization technique exploiting the length scale separation between the pores (pore-scale or microscale) and the average tissue size (the macroscale). The coefficients of the model are therefore obtained by suitable averages which involve the solutions of periodic cell problems at the pore-scale. The latter are solved numerically by finite elements in a cubic cell by assuming a cross-shaped interconnected cylindrical structure which results in a cubic symmetric stiffness tensor on the macroscale. Therefore, the macroscale response of the material is fully characterized by six parameters, namely the elastic Young's and shear moduli, Poisson's ratio, the hydraulic conductivity, and the poroelastic parameters, i.e. Biot's modulus and Biot's coefficient. We present our findings in terms of a parametric analysis conducted by varying the porosity as well as the Poisson's ratio of the matrix. Our novel three-dimensional results, which are presented in the context of tumor modeling, serve as a robust first step to (a) quantify the macroscale response of poroelastic materials on the basis of their underlying microstructure, (b) relate the compressibility of the tissue, which can be used to distinguish between benign tumor and cancer, to its microstructural properties (such as porosity), and (c) reveal a nontrivial dependency of Biot's modulus on porosity and compressibility of the matrix, which can pave the way to the optimal design of artificial constructs in terms of fluid volume available for transport of mass and solutes