Holographic Complexity Growth Rate in Horndeski Theory

Based on the context of complexity = action (CA) conjecture, we calculate the holographic complexity of AdS black holes with planar and spherical topologies in Horndeski theory. We find that the rate of change of holographic complexity for neutral AdS black holes saturates the Lloyd's bound. For charged black holes, we find that there exists only one horizon and thus the corresponding holographic complexity can't be expressed as the difference of some thermodynamical potential between two horizons as that of Reissner-Nordstrom AdS black hole in Einstein-Maxwell theory. However, the Lloyd's bound is not violated for charged AdS black hole in Horndeski theory.Comment: 20 pages, 6 figures, references added, typos correcte

Aqua­(2,2′-bipyridine)trifluorido­chromium(III) dihydrate

The title compound, [CrF3(C10H8N2)(H2O)]·2H2O, was prepared by the reaction of CrF3 and 2,2′-bipyridine under hydrous conditions. The metal centre is coordinated in a distorted octahedral mode by two N atoms from the organic ligand, three F atoms and one O atom of a water molecule. . The crystal packing is stabilized by O—H⋯O and O—H⋯F hydrogen-bonding contacts, which form a one-dimensional belt extending parallel to (100)

3-Anilino-1,3-di-2-pyridylpropan-1-one

The title compound, C19H17N3O, was prepared by the 1,4-addition reaction of 1,3-di-2-pyridylprop-2-en-1-one with aniline, and includes one chiral C atom of the methine group with an R configuration. The crystal structure is stabilized by inter­molecular N—H⋯N and C—H⋯O hydrogen bonds. The crystal structure also exhibits weak inter­molecular C—H⋯π inter­actions between a pyridyl H atom and the phenyl ring of adjacent mol­ecules

Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality

We consider Einstein-Horndeski-Maxwell gravity, together with a cosmological constant and multiple Horndeski axions. We construct charged AdS planar black holes in general dimensions where the Horndeski anxions span over the planar directions. We analyse the thermodynamics and obtain the black hole volumes. We show that the reverse isoperimetric inequality can be violated, implying that these black holes can store information more efficiently than the Schwarzschild black hole.Comment: Latex, 25 pages, 1 figure, references adde

Black Hole Entropy and Viscosity Bound in Horndeski Gravity

Horndeski gravities are theories of gravity coupled to a scalar field, in which the action contains an additional non-minimal quadratic coupling of the scalar, through its first derivative, to the Einstein tensor or the analogous higher-derivative tensors coming from the variation of Gauss-Bonnet or Lovelock terms. In this paper we study the thermodynamics of the static black hole solutions in $n$ dimensions, in the simplest case of a Horndeski coupling to the Einstein tensor. We apply the Wald formalism to calculate the entropy of the black holes, and show that there is an additional contribution over and above those that come from the standard Wald entropy formula. The extra contribution can be attributed to unusual features in the behaviour of the scalar field. We also show that a conventional regularisation to calculate the Euclidean action leads to an expression for the entropy that disagrees with the Wald results. This seems likely to be due to ambiguities in the subtraction procedure. We also calculate the viscosity in the dual CFT, and show that the viscosity/entropy ratio can violate the $\eta/S\ge 1/(4\pi)$ bound for appropriate choices of the parameters.Comment: 30 pages, no figure, minor revision

Leptonic ZZ decays in the littlest HiggsHiggs model with T-parity

The littlest $Higgs$ model with T-parity (called the $LHT$ model) predicts the existence of the T-odd leptons, which can generate contributions to some leptonic processes at the one-loop level. We calculate their contributions to the leptonic $Z$ decay processes $Z\to l\bar{l'}$, $Z\to l\bar{l}$, and Z\rightarro \nu\bar{\nu}. We find that the T-odd leptons can give significant contributions to the branching ratios of these decay processes in most of the parameter space. The experimental measurement values might generate constraints on the free parameters of the $LHT$ model.Comment: 16 pages, 8 figures, minor corrections; final version published in Phys.Rev.

Minus total domination in graphs

summary:A three-valued function $f\: V\rightarrow \{-1,0,1\}$ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f(N(v))\ge 1$, where $N(v)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f(V)=\sum f(v)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted $\gamma _t^{-}(G)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain a few lower bounds for $\gamma _t^{-}(G)$