Static Two-Body Potential at Fifth Post-Newtonian Order.

Area of Science:

• Gravitational physics
• General relativity
• Effective field theory

Background:

• Understanding gravitational interactions is crucial in astrophysics and cosmology.
• Previous calculations of gravitational potentials were limited in precision.
• The post-Newtonian (PN) expansion provides a framework for approximating general relativistic effects.

Purpose of the Study:

• To determine the static gravitational interaction between two compact bodies to the sixth power of Newton's constant (G_{N}).
• To develop a method for calculating higher-order PN contributions efficiently.
• To present a novel 5PN static potential.

Main Methods:

• Utilized the effective field theory (EFT) approach to general relativity.
• Exploited a factorization property of static diagrams for recursive calculations.
• Recomputed 1PN and 3PN static potentials and derived the 5PN contribution.

Main Results:

• Successfully calculated the gravitational interaction up to the 5PN order in the static limit.
• Demonstrated a method to derive (2n+1)PN contributions from lower-order terms.
• Presented the novel 5PN static potential.

Conclusions:

• The EFT approach combined with diagram factorization provides an efficient method for calculating higher-order gravitational potentials.
• The derived 5PN potential advances the precision of gravitational interaction calculations.
• This work contributes to a more accurate understanding of compact body interactions in strong gravitational fields.