Phase diagram of the charged black hole bomb system

We find the phase diagram of solutions of the charged black hole bomb system. In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar theory confined in a Minkowski box. We impose boundary conditions such that the scalar field vanishes at and outside a cavity of constant radius. These hairy black holes are asymptotically flat with a scalar condensate floating above the horizon. We identify four critical scalar charges which mark significant changes in the qualitative features of the phase diagram. When they coexist, hairy black holes always have higher entropy than the Reissner-Nordström black hole with the same quasilocal mass and charge. So hairy black holes are natural candidates for the endpoint of the superradiant/near-horizon instabilities of the black hole bomb system. We also relate hairy black holes to the boson stars of the theory. When it has a zero horizon radius limit, the hairy black hole family terminates on the boson star family. Finally, we find the Israel surface tensor of the box required to confine the scalar condensate and that it can obey suitable energy conditions.

A new upper bound for the largest growth rate of linear Rayleigh–Taylor instability

We investigate the effect of (interface) surface tensor on the linear Rayleigh–Taylor (RT) instability in stratified incompressible viscous fluids. The existence of linear RT instability solutions with largest growth rate Λ is proved under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold $\vartheta _{\mathrm{c}}$ ϑ c ) by the modified variational method of PDEs. Moreover, we find a new upper bound for Λ. In particular, we directly observe from the upper bound that Λ decreasingly converges to zero as ϑ goes from zero to the threshold $\vartheta _{\mathrm{c}}$ ϑ c .

Surface Energy for Nematic Liquid Crystals: A New Point of View

The surface energy of nematic liquid crystals is deduced from a phenomenological point of view. The idea of an easy surface tensor order parameter is proposed. An expression similar to a Landau expansion for the free energy of a system characterized by two order parameters is deduced and analysed. An interpretation similar to the one usually accepted for magnetic materials is given. The possibility of surface transitions induced by temperature is discussed.