  Ultra-hot Jupiters (UHJs) have recently been the focus of several atmospheric
studies due to their extreme properties. While molecular hydrogen (H$_2$) plays
a key role in UHJ atmospheres, it has not been directly detected on an
exoplanet. To determine the feasibility of H$_2$ detection via transmission
spectroscopy of the Lyman and Werner bands, we modeled UHJ atmospheres with
H$_2$ rotational temperatures varying from 2000 K to 4000 K orbiting A-type
stars ranging from $T_{eff}$ = 8,500 K to $T_{eff}$ = 10,300 K. We present
simulated transmission spectra for each planet-star temperature combination
while adding Poisson noise varying in magnitude from 0.5% to 2.0%. Finally, we
cross-correlated the spectra with expected atmospheric H$_2$ absorption
templates for each temperature combination. Our results suggest that H$_2$
detection with current facilities, namely the Hubble Space Telescope, is not
possible. However, direct atmospheric transmission spectroscopy of H$_2$ may be
viable with future UV-capable flagship missions.
