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

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.