Global Structure of Exact Scalar Hairy Dynamical Black Holes

We study the global structure of some exact scalar hairy dynamical black holes which were constructed in Einstein gravity either minimally or non-minimally coupled to a scalar field. We find that both the apparent horizon and the local event horizon (measured in luminosity coordinate) monotonically increase with the advanced time as well as the Vaidya mass. At late advanced times, the apparent horizon approaches the event horizon and gradually becomes future outer. Correspondingly, the space-time arrives at stationary black hole states with the relaxation time inversely proportional to the $1/(n-1)$ power of the final black hole mass, where $n$ is the space-time dimension. These results strongly support the solutions describing the formation of black holes with scalar hair. We also obtain new charged dynamical solutions in the non-minimal theory by introducing an Maxwell field which is non-minimally coupled to the scalar. The presence of the electric charge strongly modifies the dynamical evolution of the space-time.Comment: 18 pages and 6 figures; minor corrections, publised versio

Criticality in Einstein-Gauss-Bonnet Gravity: Gravity without Graviton

General Einstein-Gauss-Bonnet gravity with a cosmological constant allows two (A)dS spacetimes as its vacuum solutions. We find a critical point in the parameter space where the two (A)dS spacetimes coalesce into one and the linearized perturbations lack any bilinear kinetic terms. The vacuum perturbations hence loose their interpretation as linear graviton modes at the critical point. Nevertheless, the critical theory admits black hole solutions due to the nonlinear effect. We also consider Einstein gravity extended with general quadratic curvature invariants and obtain critical points where the theory has no bilinear kinetic terms for either the scalar trace mode or the transverse modes. Such critical phenomena are expected to occur frequently in general higher derivative gravities.Comment: 21 pages, no figures;refereces adde

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.Comment: 5 pages and 3 figure

Boron Nitride Nanosheets for Metal Protection

Although the high impermeability of graphene makes it an excellent barrier to inhibit metal oxidation and corrosion, graphene can form a galvanic cell with the underlying metal that promotes corrosion of the metal in the long term. Boron nitride (BN) nanosheets which have a similar impermeability could be a better choice as protective barrier, because they are more thermally and chemically stable than graphene and, more importantly, do not cause galvanic corrosion due to their electrical insulation. In this study, the performance of commercially available BN nanosheets grown by chemical vapor deposition as a protective coating on metal has been investigated. The heating of the copper foil covered with the BN nanosheet at 250 {\deg}C in air over 100 h results in dramatically less oxidation than the bare copper foil heated for 2 h under the same conditions. The electrochemical analyses reveal that the BN nanosheet coating can increase open circuit potential and possibly reduce oxidation of the underlying copper foil in sodium chloride solution. These results indicate that BN nanosheets are a good candidate for oxidation and corrosion protection, although conductive atomic force microscopy analyses show that the effectiveness of the protection relies on the quality of BN nanosheets.Comment: With Supporting Informatio