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Compact binary systems with spinning components are considered. Finite size effects due to rotational deformation are taken into account. The dynamical evolution and next to leading order gravitational wave forms are calculated, taking into…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Dörte Hansen

This work is based on the letter Phys. Lett. B, 865, 139484 (2025), where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian order in General Relativity for a compact…

General Relativity and Quantum Cosmology · Physics 2026-01-14 Vittorio De Falco , Marco Gallo

Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Robert Beig , J. Mark Heinzle , Bernd G. Schmidt

Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…

Astrophysics · Physics 2007-05-23 Douglas C. Heggie

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries…

Mathematical Physics · Physics 2011-06-07 H. Jiménez-Pérez , E. Lacomba

The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime---that is, where one mass is significantly smaller than the other---in the full context of our contemporary theory of gravity,…

General Relativity and Quantum Cosmology · Physics 2019-12-16 Marius Oltean

A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Thibault Damour , Piotr Jaranowski , Gerhard Schäfer

We introduce a -- somewhat holographic -- dictionary between gravitational observables for scattering processes (measured at the "boundary") and adiabatic invariants for bound orbits (in the "bulk"), to all orders in the Post-Minkowskian…

High Energy Physics - Theory · Physics 2020-06-03 Gregor Kälin , Rafael A. Porto

We offer an analytical study on the dynamics of a two-body problem perturbed by small post-Newtonian relativistic term. We prove that, while the angular momentum is not conserved, the motion is planar. We also show that the energy is…

Solar and Stellar Astrophysics · Physics 2016-01-20 Elbaz. I. Abouelmagd , S. M Elshaboury , H. H. Selim

In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…

Instrumentation and Methods for Astrophysics · Physics 2015-05-13 András Pál

We compute the leading Post-Newtonian (PN) contributions at quadratic order in the spins to the radiation-reaction acceleration and spin evolution for binary systems, entering at four-and-a-half PN order. Our calculation includes the…

General Relativity and Quantum Cosmology · Physics 2017-11-08 Natália T. Maia , Chad R. Galley , Adam K. Leibovich , Rafael A. Porto

The dynamics of a binary system with two spinning components on an eccentric orbit is studied, with the inclusion of the spin-spin interaction terms appearing at the second post-Newtonian order. A generalized true anomaly parametrization…

General Relativity and Quantum Cosmology · Physics 2009-10-31 László Á. Gergely

A detailed account is given on approximation schemes to the Einstein theory of general relativity where the iteration starts from the Newton theory of gravity. Two different coordinate conditions are used to represent the Einstein field…

General Relativity and Quantum Cosmology · Physics 2024-05-19 Gerhard Schäfer

In the $\Lambda$CDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second-order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The…

General Relativity and Quantum Cosmology · Physics 2017-09-11 Ruslan Brilenkov , Maxim Eingorn

A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…

General Relativity and Quantum Cosmology · Physics 2012-01-10 Hernando Quevedo

We survey theoretical and experimental/observational results on general-relativistic spin (rotation) effects in binary systems. A detailed discussion is given of the two-body Kepler problem and its first post-Newtonian generalization,…

General Relativity and Quantum Cosmology · Physics 2009-09-21 R. F. O'Connell

The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance…

General Relativity and Quantum Cosmology · Physics 2020-07-21 Sergei M. Kopeikin

An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference…

General Relativity and Quantum Cosmology · Physics 2009-10-22 C. Lübbe , J. A. Valiente Kroon

In this paper we look at the gravitational spin--spin interaction between macroscopic astronomical bodies. In particular, we calculate their post--Newtonian orbital effects of order $\mathcal{O}(c^{-2})$ on the trajectory of a spinning…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Lorenzo Iorio

We derived the second post-Newtonian solution for the quasi-Keplerian motion of a charged test particle in the Reissner-Nordstr\"om spacetime under the harmonic coordinates. The solution is formulated in terms of the test particle's orbital…

General Relativity and Quantum Cosmology · Physics 2022-03-14 Bo Yang , Chunhua Jiang , Wenbin Lin