scholarly journals Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling

2007 ◽  
Vol 75 (6) ◽  
Author(s):  
Han Wang ◽  
Clifford M. Will
Keyword(s):  
Gravitational Radiation ◽  
Binary Systems ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Einstein Equations ◽  
Spin Coupling ◽  
Direct Integration ◽  
Spin Spin Coupling

scholarly journals A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 584
Author(s):  
Xu-Hui Cheng ◽  
Guo-Qing Huang
Keyword(s):  
Binary Systems ◽  
Equations Of Motion ◽  
Exact Result ◽  
Spin Coupling ◽  
Spin Orbit Coupling ◽  
Compact Binaries ◽  
Numerical Investigations ◽  
Compact Binary ◽  
The Difference ◽  
Spin Spin Coupling

In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison with Hamiltonian approaches and approximate Lagrangian approaches at the same condition and same PN order. The completely opposite nature of the dynamics shows that using an approximate PN Lagrangian is not convincing. Hence, using the coherent PN Lagrangian is necessary for obtaining an exact result in the research of dynamics of compact binary at certain PN order. Meanwhile, numerical investigations from the spinning compact binaries show that the 2PN term plays an important role in causing chaos in the PN Hamiltonian system.

The two-body problem and radiative losses

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Mechanical Energy ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Radiation Reaction ◽  
Compact Objects ◽  
Einstein Equations ◽  
Two Body Problem ◽  
System P ◽  
Radiative Losses ◽  
Radiation Reaction Force

This chapter begins by finding the field created by compact objects in the post-linear approximation of general relativity. The second quadrupole formula is then completely proven. Next, the chapter finds the equations of motion of the bodies in the field which they create to second order in the perturbations, assuming that their velocities are small. It shows that, to correctly describe the radiation reaction at 2.5 PN order, it will prove necessary to iterate Einstein equations a third time. This leads the discussion to the equations of motion, which generalize to order 1/c5 the EIH equations of order 1/c⁲. Finally, the chapter studies the effect of the radiation reaction force on the sources, and shows that there is an energy balance at 2.5 PN order between the energy radiated to infinity and the mechanical energy lost by the system.

The mutual influence of Y···N and H···H interactions in XHY···NCH···HM complexes (X = F, Cl, Br; Y = S, Se; M = Li, Na, BeH, MgH): tuning of the chalcogen bond by dihydrogen bond interaction

2016 ◽  
Vol 94 (6) ◽  
pp. 567-573
Author(s):  
Mehdi D. Esrafili ◽  
Soheila Asadollahi ◽  
Yousef Dadban Shahamat
Keyword(s):  
Ab Initio Calculations ◽  
Ab Initio ◽  
Binary Systems ◽  
Mutual Influence ◽  
Ternary Complexes ◽  
Coupling Constants ◽  
Spin Coupling ◽  
Cooperative Effects ◽  
Bonding Properties ◽  
Spin Spin Coupling

The equilibrium structures, interaction energies, and bonding properties of ternary XHY···NCH···HM complexes are studied by ab initio calculations, where X = F, Cl, Br, Y = S, Se, and M = Li, Na, BeH, MgH. The ab initio calculations are carried out at the MP2/aug-cc-pVTZ level. The results indicate that all optimized Y···N and H···H binding distances in the ternary complexes are smaller than the corresponding values in the binary systems. The calculated cooperative energies (Ecoop) are between −0.20 kcal/mol in BrHS···NCH···HBeH and −3.29 kcal/mol in FHSe···NCH···HNa. For a given Y and M, the estimated Ecoop values increase as X = F > Cl > Br. In addition, the selenium-bonded complexes exibit larger Ecoop values than those of the sulfur-bonded counterparts. The cooperativity between Y···N and H···H interactions is further analyzed by quantum theory of atoms in molecules and natural bond orbital methods. Cooperative effects make an increase in the J(Y–N) and J(H–H) spin–spin coupling constants of the ternary complexes with respect to the binary systems.

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