The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order

A bstract We utilize various computational techniques in flat and curved backgrounds to calculate the classical gravitational Compton amplitude up to the second post-Minkowskian order. Our novel result supports the use of worldline effective field theory in non-trivial background spacetimes to obtain new theoretical insights that can both enhance computational efficiency and provide useful cross-checks of results, particularly in the context of classical binary black hole mergers.