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This gravitational radiation formula for the radiant power P is:
P = (1/5)*(G/c^5)* tr(d^3q_i_j/dt^3) [1]
The trace tr is over the average of the matrix product of the tensor with
itself.
Here d^3q_i_j/dt^3 is the third time derivative of the traceless mass
quadrupole tensor q_i_j.
The constants G and c are Newton's gravitational constant and the speed
limit of causation respectively.
... Similarly, a uniformly accelerated massive
particle in an otherwise empty spacetime doesn't emit gravitational
radiation in GR since its motion can be transformed away to a comoving
frame for which the external gravitational field vanishes.
In this frame there is no gravitational radiation, so there is not any
such radiation in any other frame either. This is why the jerk rate is so
important in inducing gravitational radiation for massive particles.
... a uniformly accelerated massive
particle in an otherwise empty spacetime doesn't emit gravitational
radiation in GR since its motion can be transformed away to a comoving
frame for which the external gravitational field vanishes.
Thus it seems that whatever reasoning that would forbid a charged
particle from undergoing an infinite acceleration because of its emitted
EM radiation would also seem to apply to any localized distribution of
mass trying to undergo an infinite jerk among its parts with the only
difference being that the mass emits gravitational radiation and the
charged particle emits EM radiation instead.