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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We provide evidence that the classical scattering of two spinning black holes
is controlled by the soft expansion of exchanged gravitons. We show how an
exponentiation of Cachazo-Strominger soft factors, acting on massive
higher-spin amplitudes, can be used to find spin contributions to the
aligned-spin scattering angle through one-loop order. The extraction of the
classical limit is accomplished via the on-shell leading-singularity method and
using massive spinor-helicity variables. The three-point amplitude for
arbitrary-spin massive particles minimally coupled to gravity is expressed in
an exponential form, and in the infinite-spin limit it matches the
stress-energy tensor of the linearized Kerr solution. A four-point
gravitational Compton amplitude is obtained from an extrapolated soft theorem,
equivalent to gluing two exponential three-point amplitudes, and becomes itself
an exponential operator. The construction uses these amplitudes to: 1) recover
the known tree-level scattering angle at all orders in spin, 2) match previous
computations of the one-loop scattering angle up to quadratic order in spin, 3)
lead to new one-loop results through quartic order in spin. These connections
map the computation of higher-multipole interactions into the study of deeper
orders in the soft expansion.
