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Second-Order Self-Force Potential-Region Binary Dynamics at O(G^{5}) in Supergravity.

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We calculated graviton contributions to scattering angles in supergravity, simplifying complex calculations for general relativity. This research advances understanding of gravitational interactions at high orders.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory

Background:

  • Calculating gravitational interactions at higher orders in Newton's constant is computationally intensive.
  • Maximal supergravity offers a technically simpler framework than Einstein gravity for these calculations.
  • Self-force effects become significant at higher orders of approximation.

Purpose of the Study:

  • To compute potential-graviton contributions to the conservative scattering angle of two nonspinning bodies.
  • To tackle challenging multiloop integrals at fifth order in Newton's constant within supergravity.
  • To provide a framework applicable to general relativity calculations.

Main Methods:

  • Utilizing the scattering-amplitude framework and effective field theory.
  • Employing multiloop integration techniques, including integration by parts and differential equations.
  • Expressing the result as a series expansion around the static limit to avoid complex special functions.

Main Results:

  • The potential-graviton contributions at fifth order were computed, including second-order self-force effects.
  • A series solution for master integrals was derived, applicable to both supergravity and general relativity.
  • Nontrivial cancellations among Calabi-Yau integrals and a Heun differential equation contribution were observed.

Conclusions:

  • The study successfully computed higher-order gravitational scattering contributions using supergravity as a simplified model.
  • The derived series solution offers a practical approach to complex integral calculations in gravitational physics.
  • The findings highlight intricate cancellations and novel mathematical structures in quantum gravity.