nongravitational forces. When gravitational forces are present alone, it is important
to note that the phenomenon of preacceleration does not occur as it would be
argued by Eq. (3-25), since Eq. (3-23) shows that the nonconservative force
depends on the velocity of the particle rather than its r'.
From Eq. (3-18), the effect of radiation damping represented by FNC is
negligibly small in magnitude compared to the conservative force Fc, owing to
the dependence of FNC on the velocity of the particle. Hence, its experimental
detection would be virtually impossible, and all the discussions above on radiation
damping would be of conceptual interest only.
3.2.2 Pfenning and Poisson: Scalar, Electromagnetic, and Gravitational
Self-forces in Weakly Curved Spacetimes
Pfenning and Poisson [8] calculated the self-force experienced by a point scalar
charge q, a point electric charge e, and a point mass m moving in a weakly curved
spacetime characterized by a time-independent Newtonian potential 4. As it was
in Dewitt and Dewitt [7], the matter distribution responsible for this potential is
assumed to be bounded, so
-M (3-27)
r
at large distances r from the matter, whose total mass is M (with the convention
G = c = 1). The procedure of calculating the self-force is similar to Dewitt
and Dewitt [7], i.e. first computing the retarded Green's functions for scalar,
electromagnetic, and gravitational fields in the weakly spacetime, and then for each
case of field evaluating the I i! integral" over the particle's past world-line.
For the scalar charge, the result is
Fs = Fsc + Fsc NC
2q2 + iq 2d, (3-28)