Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-11-04
Phys.Rev. D55 (1997) 4723-4747
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
34 pages, LaTeX, 16 figures
Scientific paper
10.1103/PhysRevD.55.4723
We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the Hamiltonian is expressed for the system of two identical particles in terms of the Lambert $W$ function. The $W$ function has two real branches which join smoothly onto each other and the Hamiltonian on the principal branch reduces to the Newtonian limit for small coupling constant. On the other branch the Hamiltonian yields a new set of motions which can not be understood as relativistically correcting the Newtonian motion. The explicit trajectory in the phase space $(r, p)$ is illustrated for various values of the energy. The analysis is extended to the case of unequal masses. The full expression of metric tensor is given and the consistency between the solution of the metric and the equations of motion is rigorously proved.
Mann Robert B.
Ohta Taisuke
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