Related papers: The binary black-hole dynamics at the third-and-a-…
In the present paper, the leading-order post-Newtonian spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians are calculated. We utilize the canonical formalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable…
In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a…
The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning…
The static, i.e., linear momentum independent, part of the next-to-leading order (NLO) gravitational spin(1)-spin(1) interaction Hamiltonian within the post-Newtonian (PN) approximation is calculated from a 3-dim. covariant ansatz for the…
Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are…
We obtain the equations of motion for compact binary systems (black holes or neutron stars) in an alternative theory of gravity known as Einstein-AEther theory, which supplements the standard spacetime metric with a timelike four-vector…
The third post-Newtonian approximation to the general relativistic dynamics of two point-mass systems has been recently derived by two independent groups, using different approaches, and different coordinate systems. By explicitly…
We study the gravitational wave emission of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner Hamiltonian formulation, where we include (for the first time in this context) terms up…
The canonical Arnowitt-Deser-Misner (ADM) Hamiltonian with next-to-leading order spin-spin coupling [J. Steinhoff, S. Hergt, and G. Sch\"afer] is converted into the EOB formalism of T. Damour, P. Jaranowski, and G. Sch\"afer for the special…
We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse…
An approximate analytical and non-linear solution of the Einstein field equations is derived for a system of multiple non-rotating black holes. The associated space-time has the same asymptotic structure as the Brill-Lindquist initial data…
The relationship between the Arnowitt-Deser-Misner (ADM) field decomposition and the non-relativistic gravitational (NRG) fields attracted considerable interest recently. This paper compares the two, especially with respect to computing the…
We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
Recently, different methods succeeded in calculating the spin dynamics at higher orders in the post-Newtonian (PN) approximation. This is an essential step toward the determination of more accurate templates for gravitational waves, to be…
Building upon recent progress in applying on-shell amplitude techniques to classical observables in general relativity, we propose a closed-form formula for the conservative Hamiltonian of a spinning binary system at the 1st…
We calculate the explicit equations of motion for non-spinning compact objects to 2.5 post-Newtonian order, or O(v/c)^5 beyond Newtonian gravity, in a general class of scalar-tensor theories of gravity. We use the formalism of the Direct…
The general relativistic corrections in the equations of motion and associated energy of a binary system of point-like masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the…
We compute next-to-next-to-leading order spin contributions to the post-Newtonian equations of motion for binaries of compact objects, such as black holes or neutron stars. For maximally spinning black holes, those contributions are of…
The post-Newtonian and post-Minkowskian solutions for the motion of binary mass systems in gravity can be derived in terms of momentum expansions within effective field theory approaches. In the post-Minkowskian approach the expansion is…