Downward Terrestrial Gamma-ray Flashes (TGFs) are sub-millisecond bursts of MeV gamma rays
produced in thunderclouds. According to the Relativistic Runaway Electron Avalanche model,
gamma rays are produced, via bremsstrahlung, from electron cascades activated by a relativistic
“seed” electron. It is not clear what mechanism is responsible for the acceleration of electrons
to relativistic energies in electric discharges. To better understand the acceleration sites and
the TGF production mechanisms, it is critically important to identify the TGF source position
and geometry in the atmosphere and to study the gamma emission characteristics. The Surface
Detector of the Pierre Auger Observatory, with its 1600 water-Cherenkov detectors very sensitive
to high-energy photons and with a very fine time-sampling, is a valuable instrument to study
downward TGFs. The possibility to analyze the radiation emission in detail led to the observation
of the first TGFs with an asymmetric azimuthal structure, suggesting a complex source different
from the initially hypothesized downward beam. We report on these observations and the new
perspectives which may open with the incorporation of new instruments at the Auger site to study
lightning development alongside gamma emission, and the increasingly detailed data provided by
satellites and global lightning networks.