  The discovery of photonic hyperbolic dispersion surfaces in certain van der
Waals bonded solids, such as hexagonal boron nitride and bismuth selenide (a
topological insulator), offers intriguing possibilities for creating strongly
modified light-matter interactions. However, open problems exist in quantifying
electromagnetic field fluctuations in these media, complicating typical
approaches for modeling photonic characteristics. Here, we address this issue
by linking the identifying traits of hyperbolic response to a coupling between
longitudinal and transverse fields that can not occur in isotropic media. This
description allows us to calculate the influence of hyperbolic response on
electromagnetic fluctuations without explicitly imposing a characteristic size
(model of nonlocality), leading to formally bounded expressions so long as
material absorption is included. We then apply this framework to two exemplary
areas: the optical sum rule for modified spontaneous emission enhancement in a
general uniaxial medium, and thermal electromagnetic field fluctuations in
hexagonal boron nitride and bismuth selenide. We find that while the sum rule
is satisfied, it does not constrain the enhancement of light-matter
interactions in either case. We also show that both hexagonal boron nitride and
bismuth selenide possess broad spectral regions where the magnitude of
electromagnetic field fluctuations are over 120 times larger, and over 800
times larger along specific angular directions, than they are in vacuum.
