Energy momentum tensor, stability, and the D-term of Q-balls

We study the energy-momentum tensor of stable, meta-stable and unstable Q-balls in scalar field theories with U(1) symmetry. We calculate properties such as charge, mass, mean square radii and the constant d1 ("D-term") as functions of the phase space angular velocity omega. We discuss the limits when omega approaches the boundaries of the region in which solutions exist, and derive analytical results for the quantities in these limits. The central result of this work is the rigorous proof that d1 is strictly negative for all finite energy solutions in the Q-ball system. We also show that for Q-balls stability is a sufficient, but not necessary, condition for d1 to be negative.