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