Inelastic Black Hole Scattering from Charged Scalar Amplitudes

TL;DR

The paper shows that the leading classical gravitational radiation from inelastic black hole scattering can be obtained from a tree-level gauge-theory amplitude via the BCJ double copy. To obtain a pure gravity result, it introduces a massless adjoint ghost scalar that cancels dilaton (and axion) contributions, enabling a clean Einstein gravity amplitude. A five-point gauge-theory amplitude with massive scalars is constructed and double-copied, and a large-mass expansion connects the result to the classical radiation through gauge-invariant vectors P_12 and Q_12. This work demonstrates a concrete path for applying the double copy to classical GR, discusses dilaton removal in detail, and outlines future directions for higher-order perturbation theory and spin effects in gravitational-wave phenomenology.

Abstract

We explain how the lowest-order classical gravitational radiation produced during the inelastic scattering of two Schwarzschild black holes in General Relativity can be obtained from a tree scattering amplitude in gauge theory coupled to scalar fields. The gauge calculation is related to gravity through the double copy. We remove unwanted scalar forces which can occur in the double copy by introducing a massless scalar in the gauge theory, which is treated as a ghost in the link to gravity. We hope these methods are a step towards a direct application of the double copy at higher orders in classical perturbation theory, with the potential to greatly streamline gravity calculations for phenomenological applications.

Figures (6)

• Figure 1: Two particle scattering with the production of radiation. This is the basic structure of diagrams we will be interested in. Note that time is on the vertical axis.
• Figure 2: The five cubic diagrams for inelastic scalar scattering with gluon production in gauge theory, where time runs vertically.
• Figure 3: The three point interaction involving the massive gauge particle.
• Figure 4: Diagrams with dilatons radiated into the final state. The dilaton is represented by the double dashed line, while the graviton is the double wavy line.
• Figure 5: Types of diagram with only intermediate, virtual, dilaton states.