If I wanted to match a hickory arrow with a 90lbs spine weighing 820 grains at 30 inches long what carbon would be it's equal?

If you want to get the carbon close to that heavy physically, you'll need to front load it a lot.  I'd say a .300 spine (75-95).  If you'll settle for a 600-650 grain arrow, a .340 will probably do it, but I don't have personal experience with spines that heavy.

Check out the Grizzly Sticks.... those are much heavier.

http://www.alaskabowhunting.com/GrizzlyStik-Shafts-C5.aspx

I shoot a CX 350 cut to 31" 300 gr broadhead, 100 brass insert
785 total
Hope this helps

I have hunted with Carbon arrows weighing over 900 grains for the last several years. I shoot them from Hill Style bows ranging from 75 to 85#.

I have been using Black Eagle Outlaw shafts in both 350 and 300 spine. I start with a heavy insert 100-125 grains and then a broadhead weighing from 235 to 260 grains. I also add an aluminum footing of 2 to 2 1/2". I then use 1/4" nylon rope to fill the arrow shaft. The rope fits tight enough it does not move, does not effect spine or arrow flight. I measure the length of the shaft then subtract the length of the insert that is inside the shaft and the part of the nock that is inside the shaft. Subtract that from the shaft length and cut the rope to that length.

I have shot thousands of shots with these arrows and have never had an issue with the nock coming out or with arrow flight. Simply The best method for weighting shafts I have found.

WOW BowHunterGA now that is something I have never thought of

Nylon Rope can be a pretty broad description. I know I tried several "shaft-fillers" and they either rattled or pushed knocks off. Gave up on it. Can describe the nylon rope more? Was it 3-strand nylon or a braided/woven nylon? I know it should be basic, poly is yellow, nylon is white, manilla is tan etc.

You need to use the right rope and length and cut it 1/2" shorter and glue to back of insert. Works like that not only full length, butfor example First third or 2/3 of arrow.