  We use first-principles calculations based on many-body perturbation theory
to investigate the near-edge electronic and optical properties of
\b{eta}-Ga2O3. The fundamental band gap is indirect, but the minimum direct gap
is only 29 meV higher in energy, which explains the strong near-edge
absorption. Our calculations verify the anisotropy of the absorption onset and
explain the range (4.4-5.0 eV) of experimentally reported band-gap values. Our
results for the radiative recombination rate indicate that intrinsic light
emission in the deep-UV range is possible in this indirect-gap semiconductor at
high excitation. Our work demonstrates the applicability of \b{eta}-Ga2O3 for
deep-UV detection and emission.
