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Scattering amplitudes of elementary particles exhibit a
fascinating simplicity, which is entirely obscured in textbook
Feynman-diagram computations. While these quantities find their primary
application to collider physics, describing the dynamics of the tiniest
particles in the universe, they also characterise the interactions among
some of its heaviest objects, such as black holes. Violent collisions
among black holes occur where tremendous amounts of energy are emitted,
in the form of gravitational waves. 100 years after having been
predicted by Einstein, their extraordinary direct detection in 2015
opened a fascinating window of observation of our universe at extreme
energies never probed before, and it is now crucial to develop novel
efficient methods for highly needed high-precision predictions. Thanks
to their inherent simplicity, amplitudes are ideally suited to this
task. I will begin by reviewing the computation of a very familiar
quantity Newton's potential, from scattering amplitudes and unitarity.
I will then explain how to compute directly observable quantities such
as the scattering angle for light or for gravitons passing by a heavy
mass such as a black hole. These computations are further simplified
thanks to a remarkable, yet still mysterious connection between
scattering amplitudes of gluons (in Yang-Mills theory) and those of
gravitons (in Einstein's General relativity), known as the "double
copy", whereby the latter amplitudes can be expressed, schematically, as
sums of squares of the former -- a property that cannot be possibly
guessed by simply staring at the Lagrangians of the two theories. I will
conclude by discussing the prospects of performing computations in
Einstein gravity to higher orders in Newton's constant using a new,
gauge-invariant version of the double copy, and as an example I will
briefly discuss the computation of the scattering angle for classical
black hole scattering to third post-Minkowskian order (or O(G^3) in
Newton's constant G).