where ( is a dimensionless constant measuring the coupling of the scalar field to

the spacetime curvature, and P is a unit vector pointing in the radial direction, and

g = -t4 is the Newtonian gravitational field. Here, is introduced to imply that

the conservative term disappears when the field is minimally coupled.

 For the electric charge, the same result to Dewitt and Dewitt [7] is reproduced,


 Fem Fem N + Fem NC
 M 2 dg
 e2 + 2 d (3-29)
 r 3 3 dt

For the point mass particle, the conservative force vanishes and only the non-

conservative (radiation-reaction) force is present,

 11 -dg
 Fgr = Fgr NC = dt (3-30)

where (-) sign implies radiation "antidampini However, this result for the grav-

itational self-force has some problems of interpretation: (i) A radiation-reaction

force should not appear in the equation of motion at this level of approxima-

tion, which corresponds to 1.5 post-Newtonian order. (ii) It should not give rise

to radiation antidamping. These problems can be resolved by incorporating a

i II, I r-mediated force" into the equation of motion: the matter-mediated force

originates from a disturbed spacetime which has become locally non-vacuum due

to the changes in its mass distribution induced by the presence of a particle in the

region. It is obtained as

 11 dg
 Fmm = 6g + 1PN + 2d (3-31)
 3 dt

where the first term represents the change in the particle's Newtonian gravitational

field associated with its motion around the fixed central mass, the second term

is a post-Newtonian correction to the Newtonian force mg, and the third term is

a radiation damping term. When the two forces from Eqs. (3-30) and (3-31) are