I am sorry right away for the seemingly dumb question, but I have driven manual transmission cars all my life so I have a question about automatic gearbox and slippage at higher rpm.

Basically, I am wondering if it's harmful to the gearbox if I am climbing a hill and playing the throttle in such a way so that there is little wheel spin (I am trying not to loose traction). What happens is the engine revs to 2500-3000 rpm and only at that point the gearbox transfers torque to the wheels (due to load when climbing).

Now, if I do this in a manual transmission car, he clutch would be screwed really quickly because of higher friction of components at higher RPM.

I know auto gearboxes do not have a clutch, but is it also harmful to the components to drive like this? Is it maybe better to give more throttle and let the wheels spin, but relieve pressure on the gearbox mechanism?