Related papers: On the two-body problem in general relativity
We review some recent works on the post-Newtonian theory of slowly-moving (post-Newtonian) sources, and its application to the problems of dynamics and gravitational radiation from compact binary systems. Our current knowledge is 3PN on the…
We suggest to solve for the motion of the two body problem in General Relativity by identifying the leading violation of conserved quantities, referred to as (relativistic) anomalies, ordered by the post-Newtonian order at which they…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary…
There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…
We study the equation of motion appropriate to an inspiralling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can…
Gravitational wave observatories targeted for compact binary coalescence, such as LIGO and VIRGO, require various theoretical inputs for their efficient detection. One of such inputs are analytical description of binary dynamics at…
On the basis of Lagrangian formalism of relativistic field theory post-Newtonian equations of motion for a rotating body are derived in the frame of Feynman's quantum field gravity theory (FGT) and compared with corresponding geodesic…
We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where…
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…
Compact object clusters are likely to exist in the centre of some galaxies because of mass segregation. The high densities and velocities reached in them deserves a better understanding. The formation of binaries and their subsequent…
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
We discuss the influence of the cosmological constant on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of the…
Starting from the recently obtained 2PN accurate forms of the energy and angular momentum fluxes from inspiralling compact binaries, we deduce the gravitational radiation reaction to 2PN order beyond the quadrupole approximation - 4.5PN…
We describe the formalism to compute gravitational-wave observables for compact binaries via the effective field theory framework in combination with modern tools from collider physics. We put particular emphasis on solving the "multi-loop"…
The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently…
The relativistic two body problem is considered in terms of the action integral in the case of two interacting spinless particles and spin-$1/2$ fermions, interacting by means of vector and scalar fields. The Lagrangians governing the…
After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
As recent work continues to demonstrate, the study of relativistic scattering processes leads to valuable insights and computational tools applicable to the relativistic bound-orbit two-body problem. This is particularly relevant in the…