Spin Dependent Gravitational Tail Memory in $D=4$

Abstract

We derive the leading spin-dependent gravitational tail memory, which appears at the second post-Minkowskian (2 PM) order and behaves as $u^{-2}$ for large retarded time $u$. This result follows from classical soft graviton theorem at order $\omega \ln \omega$ as a low-frequency expansion of gravitational waveform with frequency $\omega$. First, we conjecture the result from the classical limit of quantum soft graviton theorem up to sub-subleading order in soft expansion and then we derive it for a classical scattering process without any reference to the soft graviton theorem. The final result of the gravitational waveform in the direct derivation completely agrees with the conjectured result.

42 pages, 2 figures. The discrepancy between conjectured result and the result of direct derivation has been resolved

References in corpus (6)

• The gravitational-wave memory effect
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Searching for gravitational wave memory bursts with the Parkes Pulsar Timing Array
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• Classical Soft Graviton Theorem Rewritten
• Complete set of quasi-conserved quantities for spinning particles around Kerr

Cited by in corpus (6)

• Goldilocks Modes and the Three Scattering Bases
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Next-to-eikonal corrected double graviton dressing and gravitational wave observables at $\mathcal{O}(G^2)$
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering
• On the classical limit of the (sub)${}^n$-leading soft graviton theorems in $D=4$ without deflection