  The study investigates the gravitational scattering amplitude between two
Schwarzschild black holes in a two to two interaction, focusing on the Second
Post-Minkowskian correction (2 PM). Analyzing contributions from box and
cross-box diagrams, the research interprets Feynman integrals as pairings
between twisted co-cycles and cycles. The concept of twisted (co)-homology
groups is introduced, leading to a master integral decomposition formula. The
study successfully applies intersection theory to compute coefficients of the
master integral basis, marking the first application of intersection theory in
the quantum field theoretic description of gravity. The results align with
existing literature on the 2PM correction.
