No -- you need MORE math to demonstrate that Einstein's theory predicts gravitational waves, because
$$T = 0$$ does not require that the special-relativistic solution is the only solution to the Einstein field equations, just like the charge density equaling zero doesn't require that a completely static vacuum is the only solution to Maxwell's equations.
See http://en.wikipedia.org/wiki/Gravitational_wave#Mathematics and http://en.wikipedia.org/wiki/Linearised_Einstein_field_equations for introductory material.
$$T = 0$$ does not require that the special-relativistic solution is the only solution to the Einstein field equations, just like the charge density equaling zero doesn't require that a completely static vacuum is the only solution to Maxwell's equations.
See http://en.wikipedia.org/wiki/Gravitational_wave#Mathematics and http://en.wikipedia.org/wiki/Linearised_Einstein_field_equations for introductory material.