  We explore how the gravitational self force (or ``radiation reaction''
force), acting on a pointlike test particle in curved spacetime, is modified in
a gauge transformation. We derive the general transformation law, describing
the change in the self force in terms of the infinitesimal displacement vector
associated with the gauge transformation. Based on this transformation law, we
extend the regularization prescription by Mino et al. and Quinn and Wald
(originally formulated within the harmonic gauge) to an arbitrary gauge. Then
we extend the method of mode-sum regularization (which provides a practical
means for calculating the regularized self force and was recently applied to
the harmonic-gauge gravitational self force) to an arbitrary gauge. We find
that the regularization parameters involved in this method are
gauge-independent. We also explore the gauge transformation of the self force
from the harmonic gauge to the Regge-Wheeler gauge and to the radiation gauge,
focusing attention on the regularity of these gauge transformations. We
conclude that the transformation of the self force to the Regge-Wheeler gauge
in Schwarzschild spacetime is regular for radial orbits and irregular
otherwise, whereas the transformation to the radiation gauge is irregular for
all orbits.
