Effective one-body approach to the relativistic two-body problem (original) (raw)
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Classical and quantum two-body problem in general relativity
Letters in Mathematical Physics, 1981
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 linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different 'Schwarzschild radii'. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.
The Two-body problem: Analytical results in a toy-model of relativistic gravity
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The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes with arbitrary mass ratio. We review the basic elements of this formalism and discuss its aptitude at providing accurate template waveforms to be used for gravitational wave data analysis purposes.
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In this paper a model which describes a relativistic interaction between two point particles via an action at a distance is derived from a set of hypotheses on the relativistic dynamics. From this set of hypotheses a singular Lagrangian is obtained. The aim of this paper is to find a link between the singular-Lagrangian approach and other approaches to the relativistic dynamics of two particles. The connection of this Lagrangian model with the predictive approach of the relativistic mechanics is studied, by showing that it is possible to calculate the instantaneous forces, at least in principle. An explicit canonical transformation is given, such that a subset of the new canonical variables becomes free of constraints. In this way the instant form of the relativistic dynamics found by Bakamjan and Thomas and by Foldy is recovered.
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Gravitational two-body problem—A source theory viewpoint
Annals of Physics, 1976
An analysis of the semirelativistic gravitational two-body problem based on Schwinger's source theory is given. Our treatment is purely classical but nongeometrical. Only the large distance behavior of the gravitational stress tensor is seen to be relevant for order Ge contributions. For a gravitational stress tensor that has a pure Newtonian form, only the traceless choice is seen to be consistent with Einstein's theory. We find results in agreement with the earlier results of Einstein, Infeld, and Hoffmann, and Barker and O'Connell for spin-2 graviton exchanges between Dirac particles, and with Borner, Ehlers, and Rudolph for spin precession in theories with arbitrary post-Newtonian parameter y. The source approach clearly displays the analogy between gravitational interactions and classical electrodynamics. We also discuss the general relationship between the periastron advance and spin-precession frequencies for a class of gravitation theories. Brief estimates of the various spin-precession effects are given for the Hulse-Taylor pulsar. 406
Relativistic two-body Coulomb–Breit Hamiltonian in an external weak gravitational field
Physics Letters B, 2011
A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with Fermi normal coordinates for a freely falling observer in a spacetime region where there are no background sources and ignoring the gravitational back-reaction of the system, the effective Coulomb-Breit Hamiltonian is obtained starting from the S-matrix element corresponding to the one-photon exchange between the charged fermionic currents. The contributions due to retardation are considered up to order (v/c) 2 and they are subsequently written as effective operators in the relativistic quantum mechanical Hilbert space of the system. The final Hamiltonian includes effects linear in the curvature and up to order (v/c) 2 .
Classical and Quantum Gravity, 2001
Here we present the results of applying the generalized Riemann ζ-function regularization method to the gravitational radiation reaction problem. We analyse in detail the head-on collision of two non-spinning black holes with an extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows us to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.