Post-Minkowskian Hamiltonians in Modified Theories of Gravity

Abstract

The aim of this note is to describe the computation of post-Minkwoskian Hamiltonians in modified theories of gravity. Exploiting a recent relation between amplitudes of massive scalars and Hamiltonians for relativistic point-particles, we define a post-Minkowskian potential at second order in Newton's constant arising from ${\mathcal{R}}^3$ modifications in General Relativity. Using this result we calculate the associated contribution to the scattering angle for binary black holes at second post-Minkowskian order, showing agreement in the non relativistic limit with previous results for the bending angle of a massless particle around a static massive source in ${\mathcal{R}}^3$ theories.

arXiv comment11 pages, new calculations added (v2. submitted to Physics Letter B)

References in corpus (18)

• Effective one-body approach to general relativistic two-body dynamics
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• Einsteinian cubic gravity
• Aspects of Quadratic Gravity
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Four-dimensional black holes in Einsteinian cubic gravity
• Introductory lectures on the Effective One Body formalism
• Extreme Gravity and Fundamental Physics
• Loop Amplitudes in an Extended Gravity Theory
• Diagrammar in an Extended Theory of Gravity
• $R^2$ Dark Energy in the Laboratory

Cited by in corpus (14)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• On-shell heavy particle effective theories
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• Post-Minkowskian Scattering Angle in Einstein Gravity
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Tidal effects in quantum field theory
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• Mining the Geodesic Equation for Scattering Data
• Rotating Black Holes in Cubic Gravity
• A note on the absence of $R^2$ corrections to Newton's potential
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Conservative Dynamics of Relativistic Binaries Beyond Einstein Gravity