Soft gravitational radiation from ultra-relativistic collisions at sub- and sub-sub-leading order

Abstract

Using soft-graviton theorems a well-known zero-frequency limit (ZFL) for the gravitational radiation flux $d{E}^{GW}/d\omega$ is re-derived and extended to order $\mathcal{O}(\omega )$ and $\mathcal{O}({\omega }^2)$ for arbitrary massless multi-particle collisions. The (angle-integrated, unpolarized) $\mathcal{O}(\omega )$ correction to the flux turns out to be absent in the case of two-particle elastic collisions. The $\mathcal{O}({\omega }^2)$ correction is instead non-vanishing and takes a simple general expression which is then applied to bremsstrahlung from two-particle elastic collisions. For a tree-level process the outcome is finite and consistent with expectations. Instead, if the tree-level form of the soft theorems is used at sub-sub-leading order even when the elastic amplitude needs an all-loop (eikonal) resummation, an unphysical infrared singularity occurs. Its origin can be traced to the infinite Coulomb phase of gravitational scattering in four dimensions. We briefly discuss how to get rid, in principle, of the unwanted divergences and indicate --without carrying out-- a possible procedure to find the proper correction to the naive soft theorems. Nevertheless, if a simple recipe recently proposed for handling these divergences is adopted, we find surprisingly good agreement with results obtained independently via the eikonal approach to transplanckian-energy scattering at large (small) impact parameter (deflection angle), where such Coulomb divergences explicitly cancel out.

37 pages, 1 figure, references added, points clarified

References in corpus (14)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Evidence for a New Soft Graviton Theorem
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Soft sub-leading divergences in Yang-Mills amplitudes
• Subleading soft theorem in arbitrary dimension from scattering equations
• Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering
• Locality in quantum gravity and string theory
• Towards an S-matrix Description of Gravitational Collapse
• Infrared features of gravitational scattering and radiation in the eikonal approach
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• Soft Graviton Theorem in Arbitrary Dimensions
• Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions

Cited by in corpus (2)

• Infrared features of gravitational scattering and radiation in the eikonal approach
• The Eikonal Approximation and the Gravitational Dynamics of Binary Systems