Abstract
We describe an efficient method for extracting the parts of $D$-dimensional loop integrals that are needed to derive observables in classical general relativity from scattering amplitudes. Our approach simplifies the soft-region method of integration by judiciously combining terms before the final integrations. We demonstrate the method by computing the required integrals for black-hole scattering to the second Post-Minkowskian order in Einstein gravity coupled to scalars. We also confirm recent results at the third Post-Minkowskian order regarding universality and high-energy behavior of gravitational interactions in maximal supergravity.
Highlights
The detection of gravitational waves from binary mergers [1,2] has opened a new and exciting avenue for testing Einstein’s theory of gravity at extreme energies and at relativistic velocities
Before going into the technical details of our calculation, we find it useful to highlight the origin of the additional classical terms of the soft region as compared to those of the potential region
II we review how to determine classical general relativity from scattering amplitudes
Summary
The detection of gravitational waves from binary mergers [1,2] has opened a new and exciting avenue for testing Einstein’s theory of gravity at extreme energies and at relativistic velocities. At two-loop order the calculation very neatly separates so that the final answer for the amplitude is decomposed into all the terms from the potential region plus new contributions that arise from the above mechanism. Some of these new terms at two-loop order are real and some are both imaginary and divergent. We will discuss how it is possible to expand the scattering amplitudes at second (in Sec. III A) and third (in Sec. III) post-Minkowskian order in terms of a set of classical basis integrals multiplied with coefficients determined from unitarity.
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