Some time ago, I watched another one of Anton Petrov's videos: "We just discovered fastest main sequence star in the galaxy" and in the comments, there was some debate about the possibility of fairly large objects travelling at near lightspeed, which got me wondering (Prepare for an internet physics phd rant) - if travelling fast increases the mass of an object, could black holes technically be something like, two tiny pebbles spinning around each other at near light speed?

Also, exactly what kind of an effect does the speed of spinning have on an object. Like say if earth rotated at nearly speed of light (on surface and what about say 1 meter from center, so technically the outside would be spinning even faster?) and somehow magically was able to keep from ejecting itself in to pieces in the process?