We construct quartic quasitopological gravity, a theory of gravity containing terms quartic in the curvature that yields second order differential equations in the spherically symmetric case. Up to a term proportional to the quartic term in Lovelock gravity we find a unique solution for this quartic case, valid in any dimensionality larger than 4 except 8. This case is the highest degree of curvature coupling for which explicit black hole solutions can be constructed, and we obtain and analyze the various black hole solutions that emerge from the field equations in (n + 1) dimensions.We discuss the thermodynamics of these black holes and compute their entropy as a function of the horizon radius. We then make some general remarks about K-th order quasitopological gravity, and point out that the basic structure of the solutions will be the same in any dimensionality for general K apart from particular cases. *

No abstract

The outbreak of the disease and infection in the hospital environment and medical equipment is one of the concerns of modern life. One of the effective ways for preventing and reducing the complications of infections is modification of the surface. Here, the handmade atmospheric plasma spray system is used for accumulating copper as an antibacterial agent on the 316L stainless steel substrate, which applies to hospital environment and medical equipment. As a durable coating with proper adhesion is needed on the substrate, the effect of stand-off distance (SOD) which is an important parameter of the spray on the microstructure, the hardness and adhesion of the copper coating on the 316L stainless steel were investigated. The structure and phase composition of copper depositions were investigated using scanning electron microscopy and X-ray diffraction. The adhesion and hardness of depositions are evidenced using the cross cut tester and Vickers hardness tester, respectively. The findings confirm that the voids in the coatings increase with increasing SOD, which leads to decreasing the hardness of coatings and also the adhesion strength between depositions and substrate. In addition, by increasing the SOD, the oxygen content and the size of grains in the lamellae (fine structure) of coatings also increase.

In this paper we shall elucidate some of the effects of the quartic quasitopological term for Lifshitz-symmetric black holes. The field equations of this theory are difficult to solve exactly; here we will use numerical solutions both to verify previous exact solutions for quartic quasitopological AdS black holes as well as to examine new quasitopological Lifshitz-symmetric black hole solutions, in order to determine the effect of the quartic coupling parameter on the black hole's thermodynamic behaviour. We shall find that the quartic parameter controls solutions very similarly to the cubic parameter, allowing for the construction of a theory with another free parameter which may find meaning in the phase transition behaviour of a gauge/gravity context.

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 ≤ [n/2] rotation parameters and investigate their thermodynamics. * email address: mhd@shirazu.ac.ir