3.1.4 Mino, Sasaki, and Tanaka; Quinn and Wald: Gravitational
 Radiation Reaction of Particles in Curved Spacetime

 Extending Dewitt and Brehme's approach to the gravitational tensor field

hab, the perturbation created by a point mass m from the background spacetime

gab, Mino, Sasaki, and Tanaka [4] and Quinn and Wald [5] obtained the following

equation of motion



 a1 ( h 21ad
 m a = m V 7a bcin Vbh acin ad
 2 2

 +lim m2 b c [Va Grret (z(T) b ()) V bGret"a a'b' ((), ))

 _- a dVdGe (b ), b)) a'()b' (')d', (3-12)


where Gab, (z( ), z(r')) is a bi-tensor retarded Green's function for the tensor

wave equation in curved spacetime


 V2ab + 2Rabdhcd = -1Tab, (3-13)


with the trace-reversed field defined by

 1
 hab hab (hcC) gab (3-14)
 2

and the stress-energy tensor given by


 Tab = aa ga (x, z(T)) gbl, z(X, )) a')b')(4) (x z(T)) d, (3-15)
 Jr

and with the harmonic gauge condition


 hab;b = 0. (3-16)


 It should be noted that the Abraham-Lorentz-Dirac (ALD) term ~ ('" x2a)

is absent from the equation of motion (3-12) unlike the other cases: it has been

effectively dropped off by the reduction of order procedure. The "tail" term