How can the interior pressure of compact objects affect cosmology? This paper suggests that dark energy concentrated in black hole interiors (they use an unconventional BH model) could act like a cosmological constant. Their claim is that to calculate the equation of state (EoS) of the universe the pressure must be averaged everywhere and that the extreme negative pressures in their model of blackhole interiors makes up for their relatively tiny volume.
However, my understanding is that the "average" pressure of any slow-moving compact object is zero. For example, the walls of a mirror box containing a photon gas (EoS=1/3) are under tension (EoS<0) in proportion to the amount of light energy in the box. The average EoS of the gas + walls must be zero. Curvature has an EoS of -1/3, which again cancels out the pressure in the neutronium in a neutron star. Thus the BH model is irrelevent and the BH EoS is always zero. Is there a flaw in my reasoning?
 A: I think there is no flaw in your reasoning, and the paper is wrong.
You can make an exact counterexample by starting with a pressureless FLRW manifold, removing arbitrarily many nonoverlapping spheres, and replacing each one by a spherically symmetric compact object of the same mass surrounded by Schwarzschild vacuum. The result is an exact solution (sometimes called a swiss-cheese spacetime) that expands at the same rate as the original FLRW manifold with no dependence on the internal properties of the objects.
The authors hope that the astronomical objects identified as black holes might actually be GEODEs (GEneric Objects of Dark Energy) containing concentrated $w=-1$ dark energy, which after the averaging process would account for the apparent positive $Λ$. There is no way that this can work because substituting GEODEs for black holes in the swiss cheese model won't change the expansion rate.
Their calculations assume that the geometry of spacetime isn't far from flat. In section 3.2 they say that Kerr black holes violate that assumption (apparently because $g_{tt}$ flips sign in the ergoregion). They conclude from this not that their assumption is wrong, but that the Kerr geometry is wrong! Perhaps if the geometry of spacetime really were constrained in the way they assume then the internal structure of compact objects would have long-range effects, but it's more likely that GR is correct.
