About Kaehler-Einstein metrics

Question

Let $(M,\omega)$ be a Kaehler manifold, does it exist $\alpha$ such that $\tilde{\omega}= \omega +d\alpha$ is a Kaehler-Einstein metric?

$$\Delta \rho (\tilde{\omega})+ \lambda \rho (\tilde{\omega})= \mu \tilde{\omega}$$

with $\rho$ the Ricci curvature, and $\Delta$ the Laplacian?