Subject: does gravity attract energy?

I believe the reason we say mass does not increase with velocity is because, 
although its inertial mass increases, its gravitational attraction does not.  
But, also, isn't there a paralell of magnetism in gravitation for moving 
objects due to a length (density) contration?  Is this phenomena the same as 
saying its gravitational mass has increased, or are inertial mass and 
gravitational mass only proportional by G at low velocities?

but my real question is this:  If the attration between two bodies does 
increase with velocity due to gravi-magnetism, this attraction is parallel to 
an increase in kenetic energy.  And since E=mc^2, all mass is potentially 
electromagnetic energy even at rest.  I have not heard this connection 
explored and wondered if there is a greater body of thought out there which 
connects gravitation and energy (electromagnetic and otherwise).  It seems 
that somebody must be exploring this to try to connect relativity and the 
electromagnetic force but i can't find anything about it.

Re: does gravity attract energy?