Look at this websitewww.spacetimemodel.com It says that mass is really just a 4d volume of spacetime displacing and therefore warping the spacetime around it and so the answer is all mass displaces and so warps spacetime.
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SpaceTime - software - was created on 2007-06-04.
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There is no such thing as gravitational force. Mass curves
spacetime and stuff moves through spacetime in straight spacetime
paths. The effect of this is what we call gravity. The more the
mass the greater the curvature of spacetime.