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A Young-Laplace law for black hole horizons

Max-Planck-Institut für Gravitationsphysik, Albert Einstein Institut, Am Mühlenberg 1, D-14476 Potsdam, Germany

Phys. Rev. D 89, 021502(R) – Published 22 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.021502

Abstract

Black hole horizon sections, modeled as marginally outer trapped surfaces (MOTS), possess a notion of stability admitting a spectral characterization. Specifically, the “principal eigenvalue” $λ_{o}$ of the MOTS-stability operator (an elliptic operator on horizon sections) must be nonnegative. We discuss the expression of $λ_{o}$ 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 $λ_{o}$ is identified with a formal pressure difference between the inner and outer sides of the “bubble.” In this view, which 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.

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A Young-Laplace law for black hole horizons

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