Can UV meet IR in the Swiss cheese?

We consider the embedding of regular black holes in an expanding universe and study how the ultraviolet modifications to the Schwarzschild geometry that regularize the black hole singularity affect the exterior universe’s expansion rate. We consider several proposals for the regular black hole geometry and obtain the corresponding Friedmann equations for a universe filled only with dust and black holes. We show that different proposals have different implications which may be distinguished. We then test the hypothesis that the UV corrections to the black hole geometry may be responsible for the current phase of accelerated expansion. To this aim we constrain the value of the regular black hole UV cutoff parameter from observations. Interestingly we find that the best fit is obtained by values of the parameter corresponding to regular horizonless compact objects.

💡 Research Summary

The paper investigates whether ultraviolet (UV) modifications to black‑hole geometry—introduced to regularize the central singularity—can have infrared (IR) consequences that affect the large‑scale expansion of the universe. The authors embed several regular (non‑singular) black‑hole solutions into a Friedmann‑Lemaître‑Robertson‑Walker (FLRW) dust universe using the classic Swiss‑cheese construction, which matches an interior static spherically symmetric spacetime to an exterior expanding one across a spherical boundary.

First, the general Darmois‑Israel matching conditions are reviewed. The interior metric is written as
(ds_-^2 = -f(R)dT^2 + dR^2/f(R) + R^2 d\Omega^2) with (f(R)=1-2M(R)/R), where the mass function (M(R)) encodes any deviation from the Schwarzschild case. The exterior metric is the usual FLRW line element with scale factor (a(t)) and curvature (k). By imposing continuity of the induced metric and extrinsic curvature on a comoving boundary (constant comoving radius (r_b)), the authors derive a simple relation (f(R_b)=1-kr_b^2 - r_b^2\dot a^2/a^2).

They then parametrize the mass function as (M(R)=M_{\rm bh}