# A charged particle in constant gravitational field

In classical electrodynamics a paradox arises when we compare the power radiated by a charge falling under gravity using larmor formula (proportional to square of the acceleration, hence g^2) but the radiation reaction , given by abraham lorentz formula gives zero.(since it depends on the time derivative of the acceleration) ie. the external power required to counteract the radiation reaction is zero. I havent come across any good explanation. Can someone please help me out? Thanks.