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Scattering amplitudes, black holes and leading singularities in cubic theories of gravity. (English) Zbl 1431.83048
Summary: We compute the semi-classical potential arising from a generic theory of cubic gravity, a higher derivative theory of spin-2 particles, in the framework of modern amplitude techniques. We show that there are several interesting aspects of the potential, including some non-dispersive terms that lead to black hole solutions (including quantum corrections) that agree with those derived in Einsteinian cubic gravity (ECG). We show that these non-dispersive terms could be obtained from theories that include the Gauss-Bonnet cubic invariant \(G_3\). In addition, we derive the one-loop scattering amplitudes using both unitarity cuts and via the leading singularity, showing that the classical effects of higher derivative gravity can be easily obtained directly from the leading singularity with far less computational cost.

MSC:
83C45 Quantization of the gravitational field
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81U05 \(2\)-body potential quantum scattering theory
83C57 Black holes
83C75 Space-time singularities, cosmic censorship, etc.
Software:
xTensor; Invar; Package-X
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