Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders
Christoph Dlapa, Gregor Kälin, Zhengwen Liu, Rafael A. Porto
TLDR
This paper uses worldline EFT to derive nonlocal-in-time gravitational scattering contributions to 5PM/10SF orders, introducing the SpideR algorithm.
Key contributions
- Derives nonlocal-in-time conservative contributions in gravitational scattering to 5PM and 10SF orders.
- Introduces a novel integration-by-parts algorithm, Sparse Integral Reducer (SpideR), for complex computations.
- Results feature multiple polylogarithms up to weight three, demonstrating advanced mathematical complexity.
- Achieves perfect agreement with existing literature, validating the new 5PM/10SF order calculations.
Why it matters
This work significantly advances our understanding of gravitational scattering by calculating nonlocal-in-time tail effects at unprecedented 5PM and 10SF orders. It introduces novel computational techniques, including the SpideR algorithm, crucial for future high-precision gravitational wave predictions. These results are vital for accurately modeling binary inspirals.
Original Abstract
Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to fifth Post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight three. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the Sparse Integral Reducer (SpideR). We find perfect agreement in the overlap with all existing literature through sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at 5PM order.
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