n-body problem in general relativity up to the second post-Newtonian order from perturbative field theory
- CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7079 (United States)
Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective Lagrangian for its n-body problem. Perturbation theory is performed about a background Minkowski space-time to O[(v/c){sup 4}] beyond Newtonian gravity, where v is the typical speed of these n particles in their center of energy frame. For the specific case of the 2-body problem, the major efforts underway to measure gravitational waves produced by inspiraling compact astrophysical binaries require their gravitational interactions to be computed beyond the currently known O[(v/c){sup 7}]. We argue that such higher order post-Newtonian calculations must be automated for these field theoretic methods to be applied successfully to achieve this goal. In view of this, we outline an algorithm that would in principle generate the relevant Feynman diagrams to an arbitrary order in v/c and take steps to develop the necessary software. The Feynman diagrams contributing to the n-body effective action at O[(v/c){sup 6}] beyond Newton are derived.
- OSTI ID:
- 21260014
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 4; Other Information: DOI: 10.1103/PhysRevD.79.044031; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ALGORITHMS
ASTROPHYSICS
CLASSICAL MECHANICS
COMPUTER CODES
COMPUTERIZED SIMULATION
FEYNMAN DIAGRAM
GENERAL RELATIVITY THEORY
GRAVITATION
GRAVITATIONAL INTERACTIONS
GRAVITATIONAL WAVES
LAGRANGIAN FUNCTION
MANY-BODY PROBLEM
MINKOWSKI SPACE
PARTICLES
PERTURBATION THEORY
QUANTUM FIELD THEORY
SPACE-TIME
VELOCITY