Effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order

Abstract

We determine the general local-in-time effective-one-body (EOB) Hamiltonian for massless Scalar-Tensor (ST) theories at third post-Newtonian (PN) order. Starting from the Lagrangian derived in [Phys. Rev. D 99, 044047 (2019)], we map it to the corresponding ordinary Hamiltonian describing the two-body interaction in ST theories at 3PN level. Using a canonical transformation, we then map this onto an EOB Hamiltonian so as to determine the ST corrections to the 3PN-accurate EOB potentials $(A,B,Q_e)$ at 3PN. We then focus on circular orbits and compare the effect of the newly computed 3PN terms, also completed with finite-size and nonlocal-in-time contributions, on predictions for the frequency at the innermost stable circular orbit. Our results will be useful to build high-accuracy waveform models in ST theory, which could be used to perform precise tests against General Relativity using gravitational wave data from coalescing compact binaries.

17 pages, 2 figures, 1 Table

References in corpus (22)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• The relativistic pulsar-white dwarf binary PSR J1738+0333 II. The most stringent test of scalar-tensor gravity
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Neutron-star mergers in scalar-tensor theories of gravity
• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• Fourth post-Newtonian effective one-body dynamics
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Effective-one-body multipolar waveforms for eccentric binary black holes with non-precessing spins
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux
• Effective-one-body waveforms for precessing coalescing compact binaries with post-newtonian Twist
• Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order
• Strong-field scattering of two black holes: Numerical Relativity meets Post-Minkowskian gravity
• Dynamics of compact binary systems in scalar-tensor theories: II. Center-of-mass and conserved quantities to 3PN order
• Machine Learning Gravitational Waves from Binary Black Hole Mergers
• New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries
• Resonant tides in binary neutron star mergers: analytical-numerical relativity study
• Nonlocal-in-time effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order
• Effective-action model for dynamical scalarization beyond the adiabatic approximation
• Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order
• Relativistic effects in a mildly recycled pulsar binary: PSR J1952+2630

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