Since the discovery of gravitational waves from coalescing black holes, it has become crucial to better understand gravitational two-body dynamics and associated gravitational radiation. The gravitational force is often viewed as inherently different from the other fundamental forces: general relativity being a classical theory well-suited for describing macroscopic physics but failing when quantum effects become important at small scales. Yet, general relativity shares much common ground with modern particle physics: it is the theory of a spin-2 field in much the same way that Maxwell's Electromagnetism is a theory of a spin-1 field, both propagating at the speed of light. Both can be quantized in similar ways, resulting in photons and gravitons as the force carrier particles. In this quantum framework, Feynman rules can be constructed, and gedanken quantum experiments can be set up for the scattering of gravitons. On the other hand, general relativity is often treated as a different beast because of its ability to bend spacetime and form black holes. Black holes are still poorly understood objects, yet general relativity predicts them to be simple, characterized only by their mass, angular momentum and charge! Naively, this makes them remarkably similar to elementary particles, which, unlike black holes, have no internal structure.
In this talk I will treat general relativity akin to a quantum field theory, and introduce some modern methods and perspectives that allow for the computation of graviton scattering amplitudes with striking ease. It relies on recent advances where the mathematical structure of scattering amplitudes are found to be almost identical for gravity and the better-understood strong force, the latter being mediated by spin-1 particles called gluons. I will discuss some recent applications to analytical studies of gravitational two-body dynamics and gravitational radiation. Interestingly, modeling the black holes as elementary particles and computing their quantum amplitudes works surprisingly well. I will discuss the simplest amplitudes for both Schwarzschild and Kerr black holes.