Exactly Solvable Electrodynamic Two‐Body Problem

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

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The two-body problem: an effective-one-body approach

10.1093/oso/9780198786399.003.0056 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Body Problem ◽

Equations Of Motion ◽

Reaction Force ◽

Kerr Black Hole ◽

Radiation Reaction ◽

Spherically Symmetric ◽

Geodesic Motion ◽

Two Body Problem ◽

Symmetric Spacetime ◽

Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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Interaction between Different Kinds of Quantum Phase Transitions

Quantum Reports ◽

10.3390/quantum3020015 ◽

2021 ◽

Vol 3 (2) ◽

pp. 253-261

Author(s):

Angel Ricardo Plastino ◽

Gustavo Luis Ferri ◽

Angelo Plastino

Keyword(s):

Phase Transitions ◽

Nuclear Physics ◽

Body Problem ◽

Quantum Phase Transitions ◽

Quantum Phase ◽

Exactly Solvable Models ◽

Solvable Models ◽

Many Body ◽

Pairing Interaction ◽

Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

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