  In this paper, we realise the charged Nariai black hole on a braneworld from
a nucleated bubble in AdS$_5$, known as the dark bubble model. Geometrically,
the black hole takes the form of a cylindrical spacetime pulling on the dark
bubble. This is realised by a brane embedding in an AdS$_5$ black string
background. Identifying the brane with a D3-brane in string theory allows us to
determine a relation between the fine structure constant and the string
coupling, $\alpha_\text{EM} = \frac{3}{2} g_s$, which was previously obtained
for a microscopic black hole. We also speculate on the consequences for the
Festina Lente bound and neutrino masses.
