The judges like an arched back not hollow just enough to feel the back muscles. It also balances the horse out makes him sit on his haunches instead of on his forehand. It will also put the rider in a more secure position say if the horse decides to do something naughty. I know how it feels when I arch my back. I use my abdominal muscles more and my horse becomes so much more balanced beneath me.
I am going to disagree - god forbid, but I am.
You do not balance your horse out by hollowing out your lower back - you balance your horse by being balanced yourself. You are out, so is your horse. The moment you hollow your lower back, you've now - again - lost your balance, and your core. Those two, make a balanced and effective rider.
Lets look at the picture - REMEMBER we MUST BE EFFECTIVE AND FUNCTIONAL - NOT PRETTY AND POSED!!
This horse is activated and moving forward which is fabulous - the rider has an effective seat, BUT it would be much more effective if she was over her horses verticle.
Her horse is on his forehand, dropped back and high back end - but can be fixed if the rider sat up taller, brough her shoulders back, carried her hands, closed her elbow angle and lifted her horse up and into her.
She is effective, but can be much more if she just tweaked a few things.
You hollow your lower back - you've become an unbalanced rider.
A more secure position - is achieved through being balanced, and anchored via correct legs and heels.
If this horse in the picture made a move - I guarantee you she would be planted tight in her tack because she is effective via seat, lower leg, lower back. Her upper body - again, needs to be taller.
You loose your function of your abs when you hollow out your lower back. Do a test right now- hollow out your lower back, how effective are your abs? Now straiten your lower back, now how much more effective are your abs?