Abstract

Next-generation gravitational wave detectors require highly precise theoretical predictions for the dynamics of compact binary systems. In the initial inspiral phase where the black holes or neutron stars are far from each other, general relativity can be treated perturbatively. Solving Einstein’s equations classically is challenging due to the nonlinear nature of gravity. As an alternative, we achieve new advances by computing gauge-invariant scattering amplitudes in second-quantized Einstein gravity and taking appropriate classical limits. Our methods are particularly effective in obtaining results in the post-Minkowskian expansion, which expands in the gravitational coupling constant without a further expansion around small velocities. Novel results include conservative two-body dynamics through O(G^{4) without spin and through O(G}3) with spin, as well as dissipative dynamics such as energy loss. A variety of modern methods for scattering amplitudes, including the double copy construction, generalized unitarity and loop integration methods developed in the context of collider physics, are harnessed to enable our calculations.