We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the de Sitter metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, $P=P(\rho )$, for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $P(\rho )$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $P(\rho )$ has a root and a maximum as it approaches $0^{+}$ at large distances. Consequently, the square of the sound speed of perturbations, $c_s^2$, changes sign at the point where $P$ reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on $c_s$ puts strong constraints on the model parameters, excluding models in which the energy density has an exponential falloff. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which $P$ has its root, and at which $P$ attains its maximum.

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• Classical black holes
• Singularities In general relativity