  The LIGO-Virgo-KAGRA (LVK) collaboration has recently made it possible for
early warning alerts to be sent out, potentially before the end of the
gravitational wave (GW) emission from a neutron star binary. If we get such
alerts in this (the fourth) or the next observing run they may arrive up to
tens of seconds before the merger, which is comparable to the slewing times of
the Large Size Telescopes (designed to observe very high energy gamma rays): it
would be therefore possible to point to the source right before it starts
emitting an electromagnetic signal. This new mode of observation would allow us
to detect the TeV component of prompt emission, which is currently poorly
constrained and understood. There are many technical challenges to overcome
before this can be realized: improving the synergy between gravitational
observatories and telescopes, reducing operational latencies and, from the
gravitational wave side, providing more information, such as real-time updates
on early warning candidates and the probability distribution of the inclination
angle. Although we may need to wait a few years -- in the worst case scenario,
until the next generation of GW detectors is built -- before the first
detection of this kind is made, implementing these improvements is a necessity.
