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We analyze the role of boundary geometry in viscous electronic hydrodynamics. We address the twin questions of how boundary geometry impacts flow profiles, and how one can engineer boundary conditions -in particular the effective slip parameter -to manipulate the flow in a controlled way. We first propose a micropatterned geometry involving finned barriers, for which we show by an explicit solution that one can obtain effectively no-slip boundary conditions regardless of the detailed microscopic nature of the channel surface. Next we analyse the role of mesoscopic boundary curvature on the effective slip length, in particular its impact on the Gurzhi effect. Finally we investigate a hydrodynamic flow through a circular junction, providing a solution, which suggests an experimental set-up for determining the slip parameter. We find that its transport properties differ qualitatively from the case of ballistic conduction, and thus presents a promising setting for distinguishing the two.

A simple regular black hole solution satisfying the weak energy condition is obtained within Einsteinnon-linear electrodynamics theory. We have computed the thermodynamic properties of this black hole by a careful analysis of the horizons and we have found that the usual Bekenstein-Hawking entropy gets corrected by a logarithmic term. Therefore, in this sense our model realises some quantum gravity predictions which add this kind of correction to the black hole entropy. In particular, we have established some similitudes between our model and a quadratic generalised uncertainty principle. This similitude has been confirmed by the existence of a remnant, which prevents complete evaporation, in agreement with the quadratic generalised uncertainty principle case.

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