Exact solution for the metric and the motion of two bodies in (1+1)dimensional gravity
Abstract
We present the exact solution of twobody 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 a small coupling constant. On the other branch the Hamiltonian yields a new set of motions which cannot 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.
 Publication:

Physical Review D
 Pub Date:
 April 1997
 DOI:
 10.1103/PhysRevD.55.4723
 arXiv:
 arXiv:grqc/9611008
 Bibcode:
 1997PhRvD..55.4723M
 Keywords:

 04.50.+h;
 04.20.Cv;
 04.20.Jb;
 04.25.g;
 Gravity in more than four dimensions KaluzaKlein theory unified field theories;
 alternative theories of gravity;
 Fundamental problems and general formalism;
 Exact solutions;
 Approximation methods;
 equations of motion;
 General Relativity and Quantum Cosmology
 EPrint:
 34 pages, LaTeX, 16 figures