Choreographic solution to the general relativistic three-body problem

Abstract

We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and re-discovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general relativistic effects admit a choreographic solution such as the figure eight. We carefully examine general relativistic corrections to initial conditions so that an orbit for a three-body system can be closed and a figure eight. This solution is still choreographic. This illustration suggests that the general relativistic N-body problem also may admit a certain class of choreographic solutions.

10 pages, 4 figures, text improved, accepted for publication in PRL

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Cited by in corpus (16)

• Three Classes of Newtonian Three-Body Planar Periodic Orbits
• The three-body problem
• The 1223 new periodic orbits of planar three-body problem with unequal mass and zero angular momentum
• Numerical evolution of multiple black holes with accurate initial data
• Three-body equations of motion in successive post-Newtonian approximations
• Characterization of the gravitational wave emission of three black holes
• Gravitational wave forms, polarizations, response functions and energy losses of triple systems in Einstein-Aether theory
• Collinear solution to the general relativistic three-body problem
• Gravitational waveforms for 2- and 3-body gravitating systems
• Black-Hole Lattices as Cosmological Models
• Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects
• Gravitational wave forms for a three-body system in Lagrange's orbit: parameter determinations and a binary source test
• Stability and chaos of hierarchical three black hole configurations
• Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
• Uniqueness of collinear solutions for the relativistic three-body problem
• Approximate action-angle variables for the figure-eight and other periodic three-body orbits