Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order

Area of Science:

• Gravitational Physics
• General Relativity
• Black Hole Dynamics

Background:

• Understanding black hole mergers is crucial for gravitational wave astronomy.
• Previous calculations reached the 4PM order, with complex elliptic integrals present.
• The self-force effect is essential for accurate waveform modeling.

Purpose of the Study:

• To compute the 5PM order contributions to black hole scattering.
• To analyze the conservative sector at first self-force order.
• To simplify the mathematical structure of gravitational scattering calculations.

Main Methods:

• Utilized the worldline quantum field theory formalism.
• Performed a challenging four-loop computation using advanced integration-by-parts and differential equation techniques.
• Employed partial fraction identities to simplify the integrand.

Main Results:

• Successfully computed the 5PM order scattering angle and impulse.
• The resulting function space for the scattering angle contains only multiple polylogarithms up to weight three.
• Observed a complete absence of elliptic integrals, unlike at the 4PM order.
• All internal and external checks, including matching with post-Newtonian literature, were passed.

Conclusions:

• The 5PM order calculation simplifies the mathematical description of black hole scattering.
• This result provides a more accurate input for gravitational waveform modeling.
• The absence of elliptic integrals at 5PM order represents a significant analytical advancement.