  Black hole horizon sections, modelled as marginally outer trapped surfaces
(MOTS), possess a notion of stability admitting a spectral characterization.
Specifically, the "principal eigenvalue" \lambda_o of the MOTS-stability
operator (an elliptic operator on horizon sections) must be non-negative. We
discuss the expression of \lambda_o for axisymmetric stationary black hole
horizons and show that, remarkably, it presents the form of the Young-Laplace
law for soap bubbles in equilibrium, if \lambda_o is identified with a formal
pressure difference between the inner and outer sides of the "bubble". In this
view, that endorses the existing fluid analogies for black hole horizons,
MOTS-stability is interpreted as a consequence of a pressure increase in the
black hole trapped region.
