source of gravity

Gravity is sourced by the energy-momentum tensor \(T_{\mu\nu}\), and one particularly compelling argument for that is that the source needs to scale with \(\gamma^2\) under Lorentz-transforms (one factor of \(\gamma\) due to length contraction and the other \(\gamma\) due to relativistic mass increase, implying that \(T_{00}\propto\rho\)): Can you think of other arguments?