How to re-project EPSG:4326 to polar projection EPSG:3411

Hello,

I have global tiff file in EPSG:4326 and wanted to re-project in EPSG:3411
(http://spatialreference.org/ref/epsg/3411/).
I used this command:

"gdalwarp -s_srs EPSG:4326 -t_srs EPSG:3411 global.tif polar.tif"

which resulted in tiff image with large black hole in the middle and some
gray content outside this black circle. I was hoping obviously for opposite
- projection inside circle and black content outside, so I guess I failed at
some point but not sure where. Can anyone suggest what may be the problem
here?

I use gdal 1.10.0 on Windows

Thanks in advance